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\n  \n 2023\n \n \n (5)\n \n \n
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\n \n\n \n \n \n \n \n \n Nonequilibrium critical dynamics of the two-dimensional \\textlessmath\\textgreater \\textlessmrow\\textgreater \\textlessmo\\textgreater±\\textless/mo\\textgreater \\textlessmi\\textgreaterJ\\textless/mi\\textgreater \\textless/mrow\\textgreater \\textless/math\\textgreater Ising model.\n \n \n \n \n\n\n \n Agrawal, R.; Cugliandolo, L. F.; Faoro, L.; Ioffe, L. B.; and Picco, M.\n\n\n \n\n\n\n Physical Review E, 108(6): 064131. dec 2023.\n \n\n\n\n
\n\n\n\n \n \n \"NonequilibriumPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n  \n \n 1 download\n \n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Agrawal2023,\nabstract = {The {\\$}\\backslashpm J{\\$} Ising model is a simple frustrated spin model, where the exchange couplings independently take the discrete value {\\$}-J{\\$} with probability {\\$}p{\\$} and {\\$}+J{\\$} with probability {\\$}1-p{\\$}. It is especially appealing due to its connection to quantum error correcting codes. Here, we investigate the nonequilibrium critical behavior of the two-dimensional {\\$}\\backslashpm J{\\$} Ising model, after a quench from different initial conditions to a critical point {\\$}T{\\_}c(p){\\$} on the paramagnetic-ferromagnetic (PF) transition line, especially, above, below and at the multicritical Nishimori point (NP). The dynamical critical exponent {\\$}z{\\_}c{\\$} seems to exhibit non-universal behavior for quenches above and below the NP, which is identified as a pre-asymptotic feature due to the repulsive fixed point at the NP. Whereas, for a quench directly to the NP, the dynamics reaches the asymptotic regime with {\\$}z{\\_}c \\backslashsimeq 6.02(6){\\$}. We also consider the geometrical spin clusters (of like spin signs) during the critical dynamics. Each universality class on the PF line is uniquely characterized by the stochastic Loewner evolution (SLE) with corresponding parameter {\\$}\\backslashkappa{\\$}. Moreover, for the critical quenches from the paramagnetic phase, the model, irrespective of the frustration, exhibits an emergent critical percolation topology at the large length scales.},\narchivePrefix = {arXiv},\narxivId = {2304.11997},\nauthor = {Agrawal, Ramgopal and Cugliandolo, Leticia F. and Faoro, Lara and Ioffe, Lev B. and Picco, Marco},\ndoi = {10.1103/PhysRevE.108.064131},\neprint = {2304.11997},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Agrawal et al. - 2023 - Nonequilibrium critical dynamics of the bi-dimensional {\\$}pm J{\\$} Ising model.pdf:pdf;:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Agrawal et al. - 2023 - Nonequilibrium critical dynamics of the two-dimensional math mrow mo±mo miJmi mrow math Ising model.pdf:pdf},\nissn = {2470-0045},\njournal = {Physical Review E},\nmonth = {dec},\nnumber = {6},\npages = {064131},\ntitle = {{Nonequilibrium critical dynamics of the two-dimensional {\\textless}math{\\textgreater} {\\textless}mrow{\\textgreater} {\\textless}mo{\\textgreater}±{\\textless}/mo{\\textgreater} {\\textless}mi{\\textgreater}J{\\textless}/mi{\\textgreater} {\\textless}/mrow{\\textgreater} {\\textless}/math{\\textgreater} Ising model}},\nurl = {http://arxiv.org/abs/2304.11997 https://journals.aps.org/pre/abstract/10.1103/PhysRevE.108.064131 https://link.aps.org/doi/10.1103/PhysRevE.108.064131},\nvolume = {108},\nyear = {2023}\n}\n
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\n The $}\\pm J{$ Ising model is a simple frustrated spin model, where the exchange couplings independently take the discrete value $}-J{$ with probability $}p{$ and $}+J{$ with probability $}1-p{$. It is especially appealing due to its connection to quantum error correcting codes. Here, we investigate the nonequilibrium critical behavior of the two-dimensional $}\\pm J{$ Ising model, after a quench from different initial conditions to a critical point $}T{_}c(p){$ on the paramagnetic-ferromagnetic (PF) transition line, especially, above, below and at the multicritical Nishimori point (NP). The dynamical critical exponent $}z{_}c{$ seems to exhibit non-universal behavior for quenches above and below the NP, which is identified as a pre-asymptotic feature due to the repulsive fixed point at the NP. Whereas, for a quench directly to the NP, the dynamics reaches the asymptotic regime with $}z{_}c \\simeq 6.02(6){$. We also consider the geometrical spin clusters (of like spin signs) during the critical dynamics. Each universality class on the PF line is uniquely characterized by the stochastic Loewner evolution (SLE) with corresponding parameter $}ąppa{$. Moreover, for the critical quenches from the paramagnetic phase, the model, irrespective of the frustration, exhibits an emergent critical percolation topology at the large length scales.\n
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\n \n\n \n \n \n \n \n \n Two-dimensional Ising and Potts model with long-range bond disorder: A renormalization group approach.\n \n \n \n \n\n\n \n Chippari, F.; Picco, M.; and Santachiara, R.\n\n\n \n\n\n\n SciPost Physics, 15(4): 135. oct 2023.\n \n\n\n\n
\n\n\n\n \n \n \"Two-dimensionalPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Chippari2023a,\nabstract = {In this paper we provide new analytic results on two-dimensional q q -Potts models ( q ≥ 2 q ≥ 2 ) in the presence of bond disorder correlations which decay algebraically with distance with exponent a a . In particular, our results are valid for the long-range bond disordered Ising model ( q=2 q = 2 ). We implement a renormalization group perturbative approach based on conformal perturbation theory. We extend to the long-range case the RG scheme used in [V. Dotsenko et al., Nucl. Phys. B 455 701-23] for the short-range disorder. Our approach is based on a 2 2 -loop order double expansion in the positive parameters (2-a) ( 2 − a ) and (q-2) ( q − 2 ) . We will show that the Weinrib-Halperin conjecture for the long-range thermal exponent can be violated for a non-Gaussian disorder. We compute the central charges of the long-range fixed points finding a very good agreement with numerical measurements.},\narchivePrefix = {arXiv},\narxivId = {2306.01887},\nauthor = {Chippari, Francesco and Picco, Marco and Santachiara, Raoul},\ndoi = {10.21468/SciPostPhys.15.4.135},\neprint = {2306.01887},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Chippari, Picco, Santachiara - 2023 - Two-dimensional Ising and Potts model with long-range bond disorder a renormalization group approa.pdf:pdf;:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Chippari, Picco, Santachiara - 2023 - Two-dimensional Ising and Potts model with long-range bond disorder A renormalization group app(2).pdf:pdf},\nissn = {2542-4653},\njournal = {SciPost Physics},\nmonth = {oct},\nnumber = {4},\npages = {135},\ntitle = {{Two-dimensional Ising and Potts model with long-range bond disorder: A renormalization group approach}},\nurl = {http://arxiv.org/abs/2306.01887 http://dx.doi.org/10.21468/SciPostPhys.15.4.135 https://scipost.org/10.21468/SciPostPhys.15.4.135},\nvolume = {15},\nyear = {2023}\n}\n
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\n In this paper we provide new analytic results on two-dimensional q q -Potts models ( q ≥ 2 q ≥ 2 ) in the presence of bond disorder correlations which decay algebraically with distance with exponent a a . In particular, our results are valid for the long-range bond disordered Ising model ( q=2 q = 2 ). We implement a renormalization group perturbative approach based on conformal perturbation theory. We extend to the long-range case the RG scheme used in [V. Dotsenko et al., Nucl. Phys. B 455 701-23] for the short-range disorder. Our approach is based on a 2 2 -loop order double expansion in the positive parameters (2-a) ( 2 − a ) and (q-2) ( q − 2 ) . We will show that the Weinrib-Halperin conjecture for the long-range thermal exponent can be violated for a non-Gaussian disorder. We compute the central charges of the long-range fixed points finding a very good agreement with numerical measurements.\n
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\n \n\n \n \n \n \n \n \n Finite-size scaling of the random-field Ising model above the upper critical dimension.\n \n \n \n \n\n\n \n Fytas, N. G.; Martín-Mayor, V.; Parisi, G.; Picco, M.; and Sourlas, N.\n\n\n \n\n\n\n Physical Review E, 108(4): 044146. oct 2023.\n \n\n\n\n
\n\n\n\n \n \n \"Finite-sizePaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Fytas2023,\nabstract = {Finite-size scaling above the upper critical dimension is a long-standing puzzle in the field of Statistical Physics. Even for pure systems various scaling theories have been suggested, partially corroborated by numerical simulations. In the present manuscript we address this problem in the even more complicated case of disordered systems. In particular, we investigate the scaling behavior of the random-field Ising model at dimension {\\$}D = 7{\\$}, i.e., above its upper critical dimension {\\$}D{\\_}{\\{}\\backslashrm u{\\}} = 6{\\$}, by employing extensive ground-state numerical simulations. Our results confirm the hypothesis that at dimensions {\\$}D {\\textgreater} D{\\_}{\\{}\\backslashrm u{\\}}{\\$}, linear length scale {\\$}L{\\$} should be replaced in finite-size scaling expressions by the effective scale {\\$}L{\\_}{\\{}\\backslashrm eff{\\}} = L{\\^{}}{\\{}D / D{\\_}{\\{}\\backslashrm u{\\}}{\\}}{\\$}. Via a fitted version of the quotients method that takes this modification, but also subleading scaling corrections into account, we compute the critical point of the transition for Gaussian random fields and provide estimates for the full set of critical exponents. Thus, our analysis indicates that this modified version of finite-size scaling is successful also in the context of the random-field problem.},\narchivePrefix = {arXiv},\narxivId = {2307.01809},\nauthor = {Fytas, Nikolaos G. and Mart{\\'{i}}n-Mayor, V{\\'{i}}ctor and Parisi, Giorgio and Picco, Marco and Sourlas, Nicolas},\ndoi = {10.1103/PhysRevE.108.044146},\neprint = {2307.01809},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Fytas et al. - 2023 - Finite-size scaling of the random-field Ising model above the upper critical dimension(2).pdf:pdf},\nissn = {2470-0045},\njournal = {Physical Review E},\nmonth = {oct},\nnumber = {4},\npages = {044146},\ntitle = {{Finite-size scaling of the random-field Ising model above the upper critical dimension}},\nurl = {http://arxiv.org/abs/2307.01809 http://dx.doi.org/10.1103/PhysRevE.108.044146 https://link.aps.org/doi/10.1103/PhysRevE.108.044146},\nvolume = {108},\nyear = {2023}\n}\n
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\n Finite-size scaling above the upper critical dimension is a long-standing puzzle in the field of Statistical Physics. Even for pure systems various scaling theories have been suggested, partially corroborated by numerical simulations. In the present manuscript we address this problem in the even more complicated case of disordered systems. In particular, we investigate the scaling behavior of the random-field Ising model at dimension $}D = 7{$, i.e., above its upper critical dimension $}D{_}{\\{}m̊ u{\\}} = 6{$, by employing extensive ground-state numerical simulations. Our results confirm the hypothesis that at dimensions $}D {\\textgreater} D{_}{\\{}m̊ u{\\}}{$, linear length scale $}L{$ should be replaced in finite-size scaling expressions by the effective scale $}L{_}{\\{}m̊ eff{\\}} = L{^}{\\{}D / D{_}{\\{}m̊ u{\\}}{\\}}{$. Via a fitted version of the quotients method that takes this modification, but also subleading scaling corrections into account, we compute the critical point of the transition for Gaussian random fields and provide estimates for the full set of critical exponents. Thus, our analysis indicates that this modified version of finite-size scaling is successful also in the context of the random-field problem.\n
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\n \n\n \n \n \n \n \n \n Long-range quenched bond disorder in the bi-dimensional Potts model.\n \n \n \n \n\n\n \n Chippari, F.; Picco, M.; and Santachiara, R.\n\n\n \n\n\n\n Journal of Statistical Mechanics: Theory and Experiment, 2023(4): 043301. jan 2023.\n \n\n\n\n
\n\n\n\n \n \n \"Long-rangePaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n  \n \n 2 downloads\n \n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Chippari2023,\nabstract = {We study the bi-dimensional {\\$}q{\\$}-Potts model with long-range bond correlated disorder. Similarly to [C. Chatelain, Phys. Rev. E 89, 032105], we implement a disorder bimodal distribution by coupling the Potts model to auxiliary spin-variables, which are correlated with a power-law decaying function. The universal behaviour of different observables, especially the thermal and the order-parameter critical exponents, are computed by Monte-Carlo techniques for {\\$}q=1,2,3{\\$}-Potts models for different values of the power-law decaying exponent {\\$}a{\\$}. On the basis of our conclusions, which are in agreement with previous theoretical and numerical results for {\\$}q=1{\\$} and {\\$}q=2{\\$}, we can conjecture the phase diagram for {\\$}q\\backslashin [1,4]{\\$}. In particular, we establish that the system is driven to a fixed point at finite or infinite long-range disorder depending on the values of {\\$}q{\\$} and {\\$}a{\\$}. Finally, we discuss the role of the higher cumulants of the disorder distribution. This is done by drawning the auxiliary spin-variables from different statistical models. While the main features of the phase diagram depend only on the first and second cumulant, we argue, for the infinite disorder fixed point, that certain universal effects are affected by the higher cumulants of the disorder distribution.},\narchivePrefix = {arXiv},\narxivId = {2301.13727},\nauthor = {Chippari, Francesco and Picco, Marco and Santachiara, Raoul},\ndoi = {10.1088/1742-5468/acc72a},\neprint = {2301.13727},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Chippari, Picco, Santachiara - 2023 - Long-range quenched bond disorder in the bidimensional Potts model.pdf:pdf},\nissn = {1742-5468},\njournal = {Journal of Statistical Mechanics: Theory and Experiment},\nmonth = {jan},\nnumber = {4},\npages = {043301},\ntitle = {{Long-range quenched bond disorder in the bi-dimensional Potts model}},\nurl = {http://arxiv.org/abs/2301.13727 https://iopscience.iop.org/article/10.1088/1742-5468/acc72a http://dx.doi.org/10.1088/1742-5468/acc72a},\nvolume = {2023},\nyear = {2023}\n}\n
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\n We study the bi-dimensional $}q{$-Potts model with long-range bond correlated disorder. Similarly to [C. Chatelain, Phys. Rev. E 89, 032105], we implement a disorder bimodal distribution by coupling the Potts model to auxiliary spin-variables, which are correlated with a power-law decaying function. The universal behaviour of different observables, especially the thermal and the order-parameter critical exponents, are computed by Monte-Carlo techniques for $}q=1,2,3{$-Potts models for different values of the power-law decaying exponent $}a{$. On the basis of our conclusions, which are in agreement with previous theoretical and numerical results for $}q=1{$ and $}q=2{$, we can conjecture the phase diagram for $}q\\in [1,4]{$. In particular, we establish that the system is driven to a fixed point at finite or infinite long-range disorder depending on the values of $}q{$ and $}a{$. Finally, we discuss the role of the higher cumulants of the disorder distribution. This is done by drawning the auxiliary spin-variables from different statistical models. While the main features of the phase diagram depend only on the first and second cumulant, we argue, for the infinite disorder fixed point, that certain universal effects are affected by the higher cumulants of the disorder distribution.\n
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\n \n\n \n \n \n \n \n \n Freezing vs. equilibration dynamics in the Potts model.\n \n \n \n \n\n\n \n Chippari, F.; and Picco, M.\n\n\n \n\n\n\n Journal of Statistical Mechanics: Theory and Experiment, 2023(2): 023201. feb 2023.\n \n\n\n\n
\n\n\n\n \n \n \"FreezingPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Chippari2022a,\nabstract = {We study the quench dynamics of the q Potts model on different bi/tri-dimensional lattice topologies. In particular, we are interested in instantaneous quench from T i → ∞ to T ⩽ T s , where T s is the (pseudo)-spinodal temperature. The goal is to explain why, in the large- q limit, the low-temperature dynamics freezes on some lattices while on others the equilibrium configuration is easily reached. The cubic (3 d ) and the triangular (2 d ) lattices are analysed in detail. We show that the dynamics blocks when lattices have acyclic unitary structures while the system goes to the equilibrium when these are cyclic, no matter the coordination number ( z ) of the particularly considered lattice.},\narchivePrefix = {arXiv},\narxivId = {2208.08770},\nauthor = {Chippari, Francesco and Picco, Marco},\ndoi = {10.1088/1742-5468/acb257},\neprint = {2208.08770},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Chippari, Picco - 2023 - Freezing vs. equilibration dynamics in the Potts model.pdf:pdf},\nissn = {1742-5468},\njournal = {Journal of Statistical Mechanics: Theory and Experiment},\nmonth = {feb},\nnumber = {2},\npages = {023201},\ntitle = {{Freezing vs. equilibration dynamics in the Potts model}},\nurl = {http://arxiv.org/abs/2208.08770 http://dx.doi.org/10.1088/1742-5468/acb257 https://iopscience.iop.org/article/10.1088/1742-5468/acb257},\nvolume = {2023},\nyear = {2023}\n}\n
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\n We study the quench dynamics of the q Potts model on different bi/tri-dimensional lattice topologies. In particular, we are interested in instantaneous quench from T i → ∞ to T ⩽ T s , where T s is the (pseudo)-spinodal temperature. The goal is to explain why, in the large- q limit, the low-temperature dynamics freezes on some lattices while on others the equilibrium configuration is easily reached. The cubic (3 d ) and the triangular (2 d ) lattices are analysed in detail. We show that the dynamics blocks when lattices have acyclic unitary structures while the system goes to the equilibrium when these are cyclic, no matter the coordination number ( z ) of the particularly considered lattice.\n
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\n \n\n \n \n \n \n \n \n How many phases nucleate in the bidimensional Potts model?.\n \n \n \n \n\n\n \n Corberi, F.; Cugliandolo, L. F.; Esposito, M.; Mazzarisi, O.; and Picco, M.\n\n\n \n\n\n\n Journal of Statistical Mechanics: Theory and Experiment, 2022(7): 073204. jul 2022.\n \n\n\n\n
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@article{Esposito2021,\nabstract = {We study the kinetics of the two-dimensional q {\\textgreater} 4-state Potts model after a shallow quench to a temperature slightly below the critical one and above the pseudo spinodal. We use numerical methods and we focus on intermediate values of q , 4 {\\textless} q ⩽ 100. We show that, initially, the system evolves as if it were quenched to the critical temperature: the configurations exhibit correlations that are indistinguishable from the ones in equilibrium at T c ( q ) over longer and longer length scales as time elapses. The further decay from the metastable state occurs by nucleation of an average number k out of the q possible phases. For a given quench temperature, k is a logarithmically increasing function of the system size, bounded by q . This unusual finite size dependence is a consequence of a scaling property underlying the nucleation phenomenon for these parameters.},\narchivePrefix = {arXiv},\narxivId = {2102.01003},\nauthor = {Corberi, Federico and Cugliandolo, Leticia F. and Esposito, Marco and Mazzarisi, Onofrio and Picco, Marco},\ndoi = {10.1088/1742-5468/ac7aa9},\neprint = {2102.01003},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Esposito et al. - 2021 - How many phases nucleate in the bidimensional Potts model.pdf:pdf},\nissn = {1742-5468},\njournal = {Journal of Statistical Mechanics: Theory and Experiment},\nmonth = {jul},\nnumber = {7},\npages = {073204},\ntitle = {{How many phases nucleate in the bidimensional Potts model?}},\nurl = {http://arxiv.org/abs/2102.01003 http://dx.doi.org/10.1088/1742-5468/ac7aa9 https://iopscience.iop.org/article/10.1088/1742-5468/ac7aa9},\nvolume = {2022},\nyear = {2022}\n}\n
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\n We study the kinetics of the two-dimensional q \\textgreater 4-state Potts model after a shallow quench to a temperature slightly below the critical one and above the pseudo spinodal. We use numerical methods and we focus on intermediate values of q , 4 \\textless q ⩽ 100. We show that, initially, the system evolves as if it were quenched to the critical temperature: the configurations exhibit correlations that are indistinguishable from the ones in equilibrium at T c ( q ) over longer and longer length scales as time elapses. The further decay from the metastable state occurs by nucleation of an average number k out of the q possible phases. For a given quench temperature, k is a logarithmically increasing function of the system size, bounded by q . This unusual finite size dependence is a consequence of a scaling property underlying the nucleation phenomenon for these parameters.\n
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\n \n\n \n \n \n \n \n \n On the CFT describing the spin clusters in 2d Potts model.\n \n \n \n \n\n\n \n Picco, M.; and Santachiara, R.\n\n\n \n\n\n\n Journal of Statistical Mechanics: Theory and Experiment, 2022(2): 023102. feb 2022.\n \n\n\n\n
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@article{Picco2021,\nabstract = {We have considered clusters of like spins in the Q -Potts model, the spin Potts clusters (S clusters). Using Monte Carlo simulations, we studied these clusters on a square lattice with periodic boundary conditions for values of Q ∈ [1, 4]. We continue the work initiated by Delfino et al (2013 J. Stat. Mech. P11011) by measuring the universal finite size corrections of the two-point connectivity. The numerical data are perfectly compatible with the conformal field theory (CFT) prediction, thus supporting the existence of a consistent CFT, still unknown, describing the connectivity Potts spin clusters. We provided in particular new insights on the energy field of such theory. For Q = 2, we found a good agreement with the prediction that the Ising spin clusters behave as the Fortuin–Kasteleyn ones at the tri-critical point of the dilute one-Potts model. We show that the structure constants are likely to be given by the imaginary Liouville structure constants, consistently with the results by Delfino et al (2013 J. Stat. Mech. P11011); Ang and Sun (2021 arXiv:2107.01788). For Q ≠ 2 instead, the structure constants we measure do not correspond to any known bootstrap solutions. The validity of our analysis is backed up by the measures of the spin Potts cluster wrapping probability for Q = 3. We evaluate the main critical exponents and the correction to the scaling. A new exact and compact expression for the torus one-point of the Q -Potts energy field is also given.},\narchivePrefix = {arXiv},\narxivId = {2111.03846},\nauthor = {Picco, Marco and Santachiara, Raoul},\ndoi = {10.1088/1742-5468/ac4c3d},\neprint = {2111.03846},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Picco, Santachiara - 2022 - On the CFT describing the spin clusters in 2d Potts model.pdf:pdf},\nissn = {1742-5468},\njournal = {Journal of Statistical Mechanics: Theory and Experiment},\nmonth = {feb},\nnumber = {2},\npages = {023102},\ntitle = {{On the CFT describing the spin clusters in 2d Potts model}},\nurl = {http://arxiv.org/abs/2111.03846 http://dx.doi.org/10.1088/1742-5468/ac4c3d https://iopscience.iop.org/article/10.1088/1742-5468/ac4c3d},\nvolume = {2022},\nyear = {2022}\n}\n
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\n We have considered clusters of like spins in the Q -Potts model, the spin Potts clusters (S clusters). Using Monte Carlo simulations, we studied these clusters on a square lattice with periodic boundary conditions for values of Q ∈ [1, 4]. We continue the work initiated by Delfino et al (2013 J. Stat. Mech. P11011) by measuring the universal finite size corrections of the two-point connectivity. The numerical data are perfectly compatible with the conformal field theory (CFT) prediction, thus supporting the existence of a consistent CFT, still unknown, describing the connectivity Potts spin clusters. We provided in particular new insights on the energy field of such theory. For Q = 2, we found a good agreement with the prediction that the Ising spin clusters behave as the Fortuin–Kasteleyn ones at the tri-critical point of the dilute one-Potts model. We show that the structure constants are likely to be given by the imaginary Liouville structure constants, consistently with the results by Delfino et al (2013 J. Stat. Mech. P11011); Ang and Sun (2021 arXiv:2107.01788). For Q ≠ 2 instead, the structure constants we measure do not correspond to any known bootstrap solutions. The validity of our analysis is backed up by the measures of the spin Potts cluster wrapping probability for Q = 3. We evaluate the main critical exponents and the correction to the scaling. A new exact and compact expression for the torus one-point of the Q -Potts energy field is also given.\n
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\n  \n 2021\n \n \n (1)\n \n \n
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\n \n\n \n \n \n \n \n \n Low-temperature universal dynamics of the bidimensional Potts model in the large q limit.\n \n \n \n \n\n\n \n Chippari, F.; Cugliandolo, L. F.; and Picco, M.\n\n\n \n\n\n\n Journal of Statistical Mechanics: Theory and Experiment, 2021(9): 093201. sep 2021.\n \n\n\n\n
\n\n\n\n \n \n \"Low-temperaturePaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n  \n \n 9 downloads\n \n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Chippari2021,\nabstract = {We study the low temperature quench dynamics of the two-dimensional Potts model in the limit of large number of states, q {\\textgreater}{\\textgreater} 1. We identify a q-independent crossover temperature (the pseudo spinodal) below which no high-temperature metastability stops the curvature driven coarsening process. At short length scales, the latter is decorated by freezing for some lattice geometries, notably the square one. With simple analytic arguments we evaluate the relevant time-scale in the coarsening regime, which turns out to be of Arrhenius form and independent of q for large q. Once taken into account dynamic scaling is universal.},\narchivePrefix = {arXiv},\narxivId = {2102.01035},\nauthor = {Chippari, Francesco and Cugliandolo, Leticia F. and Picco, Marco},\ndoi = {10.1088/1742-5468/ac0f67},\neprint = {2102.01035},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Chippari, Cugliandolo, Picco - 2021 - Low-temperature universal dynamics of the bidimensional Potts model in the large q limit.pdf:pdf},\nissn = {1742-5468},\njournal = {Journal of Statistical Mechanics: Theory and Experiment},\nmonth = {sep},\nnumber = {9},\npages = {093201},\ntitle = {{Low-temperature universal dynamics of the bidimensional Potts model in the large q limit}},\nurl = {http://arxiv.org/abs/2102.01035 https://iopscience.iop.org/article/10.1088/1742-5468/ac0f67},\nvolume = {2021},\nyear = {2021}\n}\n
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\n We study the low temperature quench dynamics of the two-dimensional Potts model in the limit of large number of states, q \\textgreater\\textgreater 1. We identify a q-independent crossover temperature (the pseudo spinodal) below which no high-temperature metastability stops the curvature driven coarsening process. At short length scales, the latter is decorated by freezing for some lattice geometries, notably the square one. With simple analytic arguments we evaluate the relevant time-scale in the coarsening regime, which turns out to be of Arrhenius form and independent of q for large q. Once taken into account dynamic scaling is universal.\n
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\n  \n 2020\n \n \n (3)\n \n \n
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\n \n\n \n \n \n \n \n \n Spin interfaces and crossing probabilities of spin clusters in parafermionic models.\n \n \n \n \n\n\n \n Fukusumi, Y.; Picco, M.; and Santachiara, R.\n\n\n \n\n\n\n . jun 2020.\n \n\n\n\n
\n\n\n\n \n \n \"SpinPaper\n  \n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Fukusumi2020,\nabstract = {We consider fractal curves in two-dimensional {\\$}Z{\\_}N{\\$} spin lattice models. These are N states spin models that undergo a continuous ferromagnetic-paramagnetic phase transition described by the ZN parafermionic field theory. The main motivation here is to investigate the correspondence between Schramm-Loewner evolutions (SLE) and conformal field theories with extended conformal algebras (ECFT). By using Monte-Carlo simulation, we compute the fractal dimension of different spin interfaces for the N=3 and N=4 spin models that correspond respectively to the 3 states Potts model and to the Ashkin-Teller model at the Fateev-Zamolodchikov point. These numerical measures, that improve and complete the ones presented in the previous works, are shown to be consistent with SLE/ECFT predictions. We consider then the crossing probability of spin clusters in a rectangular domain. Using a multiple SLE approach, we provide crossing probability formulas for ZN parafarmionic theories. The parafermionic conformal blocks that enter the crossing probability formula are computed by solving a Knhiznik-Zamolodchikov system of rank 3. In the 3 states Potts model case, where the parafermionic blocks coincide with the Virasoro ones, we rederive the crossing formula found by S.M.Flores et al., that is in good agreement with our measures. For N{\\textgreater}=4 where the crossing probability satisfies a third order differential equation instead of a second order one, our formulas are new. The theoretical predictions are compared to Monte-Carlo measures taken at N=4 and a fair agreement is found.},\narchivePrefix = {arXiv},\narxivId = {2006.09850},\nauthor = {Fukusumi, Yoshiki and Picco, Marco and Santachiara, Raoul},\neprint = {2006.09850},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Fukusumi, Picco, Santachiara - 2020 - Spin interfaces and crossing probabilities of spin clusters in parafermionic models.pdf:pdf},\nmonth = {jun},\ntitle = {{Spin interfaces and crossing probabilities of spin clusters in parafermionic models}},\nurl = {http://arxiv.org/abs/2006.09850},\nyear = {2020}\n}\n
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\n We consider fractal curves in two-dimensional $}Z{_}N{$ spin lattice models. These are N states spin models that undergo a continuous ferromagnetic-paramagnetic phase transition described by the ZN parafermionic field theory. The main motivation here is to investigate the correspondence between Schramm-Loewner evolutions (SLE) and conformal field theories with extended conformal algebras (ECFT). By using Monte-Carlo simulation, we compute the fractal dimension of different spin interfaces for the N=3 and N=4 spin models that correspond respectively to the 3 states Potts model and to the Ashkin-Teller model at the Fateev-Zamolodchikov point. These numerical measures, that improve and complete the ones presented in the previous works, are shown to be consistent with SLE/ECFT predictions. We consider then the crossing probability of spin clusters in a rectangular domain. Using a multiple SLE approach, we provide crossing probability formulas for ZN parafarmionic theories. The parafermionic conformal blocks that enter the crossing probability formula are computed by solving a Knhiznik-Zamolodchikov system of rank 3. In the 3 states Potts model case, where the parafermionic blocks coincide with the Virasoro ones, we rederive the crossing formula found by S.M.Flores et al., that is in good agreement with our measures. For N\\textgreater=4 where the crossing probability satisfies a third order differential equation instead of a second order one, our formulas are new. The theoretical predictions are compared to Monte-Carlo measures taken at N=4 and a fair agreement is found.\n
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\n \n\n \n \n \n \n \n \n Metastability in the Potts model: exact results in the large q limit.\n \n \n \n \n\n\n \n Mazzarisi, O.; Corberi, F.; Cugliandolo, L. F.; and Picco, M.\n\n\n \n\n\n\n Journal of Statistical Mechanics: Theory and Experiment, 2020(6): 063214. jul 2020.\n \n\n\n\n
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@article{Mazzarisi2020a,\nabstract = {We study the metastable equilibrium properties of the Potts model with heat-bath transition rates using a novel expansion. The method is especially powerful for large number of state spin variables and it is notably accurate in a rather wide range of temperatures around the phase transition.},\narchivePrefix = {arXiv},\narxivId = {2003.03126},\nauthor = {Mazzarisi, Onofrio and Corberi, Federico and Cugliandolo, Leticia F. and Picco, Marco},\ndoi = {10.1088/1742-5468/ab8556},\neprint = {2003.03126},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Mazzarisi et al. - 2020 - Metastability in the Potts model exact results in the large q limit.pdf:pdf;:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Mazzarisi et al. - 2020 - Metastability in the Potts model exact results in the large q limit(2).pdf:pdf},\nissn = {1742-5468},\njournal = {Journal of Statistical Mechanics: Theory and Experiment},\nmonth = {jul},\nnumber = {6},\npages = {063214},\ntitle = {{Metastability in the Potts model: exact results in the large q limit}},\nurl = {http://arxiv.org/abs/2003.03126 https://iopscience.iop.org/article/10.1088/1742-5468/ab8556},\nvolume = {2020},\nyear = {2020}\n}\n
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\n We study the metastable equilibrium properties of the Potts model with heat-bath transition rates using a novel expansion. The method is especially powerful for large number of state spin variables and it is notably accurate in a rather wide range of temperatures around the phase transition.\n
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\n \n\n \n \n \n \n \n \n Two-point connectivity of two-dimensional critical Q -Potts random clusters on the torus.\n \n \n \n \n\n\n \n Javerzat, N.; Picco, M.; and Santachiara, R.\n\n\n \n\n\n\n Journal of Statistical Mechanics: Theory and Experiment, 2020(2): 023101. feb 2020.\n \n\n\n\n
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@article{Javerzat2019,\nabstract = {We consider the two dimensional {\\$}Q-{\\$} random-cluster Potts model on the torus and at the critical point. We study the probability for two points to be connected by a cluster for general values of {\\$}Q\\backslashin [1,4]{\\$}. Using a Conformal Field Theory (CFT) approach, we provide the leading topological corrections to the plane limit of this probability. These corrections have universal nature and include, as a special case, the universality class of two-dimensional critical percolation. We compare our predictions to Monte Carlo measurements. Finally, we take Monte Carlo measurements of the torus energy one-point function that we compare to CFT computations.},\narchivePrefix = {arXiv},\narxivId = {1907.11041},\nauthor = {Javerzat, Nina and Picco, Marco and Santachiara, Raoul},\ndoi = {10.1088/1742-5468/ab6331},\neprint = {1907.11041},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Javerzat, Picco, Santachiara - 2020 - Two-point connectivity of two-dimensional critical Q -Potts random clusters on the torus.pdf:pdf;:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Javerzat, Picco, Santachiara - 2020 - Two-point connectivity of two-dimensional critical Q -Potts random clusters on the torus(2).pdf:pdf},\nissn = {1742-5468},\njournal = {Journal of Statistical Mechanics: Theory and Experiment},\nmonth = {feb},\nnumber = {2},\npages = {023101},\ntitle = {{Two-point connectivity of two-dimensional critical Q -Potts random clusters on the torus}},\nurl = {http://arxiv.org/abs/1907.11041 http://dx.doi.org/10.1088/1742-5468/ab6331},\nvolume = {2020},\nyear = {2020}\n}\n
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\n We consider the two dimensional $}Q-{$ random-cluster Potts model on the torus and at the critical point. We study the probability for two points to be connected by a cluster for general values of $}Q\\in [1,4]{$. Using a Conformal Field Theory (CFT) approach, we provide the leading topological corrections to the plane limit of this probability. These corrections have universal nature and include, as a special case, the universality class of two-dimensional critical percolation. We compare our predictions to Monte Carlo measurements. Finally, we take Monte Carlo measurements of the torus energy one-point function that we compare to CFT computations.\n
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\n  \n 2019\n \n \n (6)\n \n \n
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\n \n\n \n \n \n \n \n \n Multinucleation in the first-order phase transition of the 2d Potts model.\n \n \n \n \n\n\n \n Corberi, F.; Cugliandolo, L. F L.; Esposito, M.; and Picco, M.\n\n\n \n\n\n\n Journal of Physics: Conference Series, 1226: 012009. may 2019.\n \n\n\n\n
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@article{Corberi2019,\nabstract = {Using large-scale numerical simulations we studied the kinetics of the 2d q-Potts model for q {\\textgreater} 4 after a shallow subcritical quench from a high-temperature homogeneous configuration. This protocol drives the system across a first-order phase transition. The initial state is metastable after the quench and, for final temperatures close to the critical one, the system escapes from it via a multi-nucleation process. The ensuing relaxation towards equilibrium proceeds through coarsening with competition between the equivalent ground states. This process has been analyzed for different choices of the parameters such as the number of states and the final quench temperature.},\narchivePrefix = {arXiv},\narxivId = {1906.09803},\nauthor = {Corberi, Federico and Cugliandolo, Leticia F L.F. and Esposito, Marco and Picco, Marco},\ndoi = {10.1088/1742-6596/1226/1/012009},\neprint = {1906.09803},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Corberi et al. - 2019 - Multinucleation in the first-order phase transition of the 2d Potts model(3).pdf:pdf},\nissn = {1742-6588},\njournal = {Journal of Physics: Conference Series},\nmonth = {may},\npages = {012009},\ntitle = {{Multinucleation in the first-order phase transition of the 2d Potts model}},\nurl = {http://arxiv.org/abs/1906.09803 http://dx.doi.org/10.1088/1742-6596/1226/1/012009 https://iopscience.iop.org/article/10.1088/1742-6596/1226/1/012009},\nvolume = {1226},\nyear = {2019}\n}\n
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\n Using large-scale numerical simulations we studied the kinetics of the 2d q-Potts model for q \\textgreater 4 after a shallow subcritical quench from a high-temperature homogeneous configuration. This protocol drives the system across a first-order phase transition. The initial state is metastable after the quench and, for final temperatures close to the critical one, the system escapes from it via a multi-nucleation process. The ensuing relaxation towards equilibrium proceeds through coarsening with competition between the equivalent ground states. This process has been analyzed for different choices of the parameters such as the number of states and the final quench temperature.\n
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\n \n\n \n \n \n \n \n \n Evidence for Supersymmetry in the Random-Field Ising Model at D=5.\n \n \n \n \n\n\n \n Fytas, N. G.; Martín-Mayor, V.; Parisi, G.; Picco, M.; and Sourlas, N.\n\n\n \n\n\n\n Physical Review Letters, 122(24): 240603. jun 2019.\n \n\n\n\n
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@article{Fytas2019,\nabstract = {We provide a non-trivial test of supersymmetry in the random-field Ising model at five spatial dimensions, by means of extensive zero-temperature numerical simulations. Indeed, supersymmetry relates correlation functions in a D-dimensional disordered system with some other correlation functions in a D-2 clean system. We first show how to check these relationships in a finite-size scaling calculation, and then perform a high-accuracy test. While the supersymmetric predictions are satisfied even to our high-accuracy at D=5, they fail to describe our results at D=4.},\narchivePrefix = {arXiv},\narxivId = {1901.08473},\nauthor = {Fytas, Nikolaos G. and Mart{\\'{i}}n-Mayor, V{\\'{i}}ctor and Parisi, Giorgio and Picco, Marco and Sourlas, Nicolas},\ndoi = {10.1103/PhysRevLett.122.240603},\neprint = {1901.08473},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Fytas et al. - 2019 - Evidence for Supersymmetry in the Random-Field Ising Model at D=5.pdf:pdf;:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Fytas et al. - 2019 - Evidence for Supersymmetry in the Random-Field Ising Model at D=5(2).pdf:pdf},\nissn = {0031-9007},\njournal = {Physical Review Letters},\nmonth = {jun},\nnumber = {24},\npages = {240603},\ntitle = {{Evidence for Supersymmetry in the Random-Field Ising Model at D=5}},\nurl = {http://arxiv.org/abs/1901.08473 http://dx.doi.org/10.1103/PhysRevLett.122.240603 https://link.aps.org/doi/10.1103/PhysRevLett.122.240603},\nvolume = {122},\nyear = {2019}\n}\n
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\n We provide a non-trivial test of supersymmetry in the random-field Ising model at five spatial dimensions, by means of extensive zero-temperature numerical simulations. Indeed, supersymmetry relates correlation functions in a D-dimensional disordered system with some other correlation functions in a D-2 clean system. We first show how to check these relationships in a finite-size scaling calculation, and then perform a high-accuracy test. While the supersymmetric predictions are satisfied even to our high-accuracy at D=5, they fail to describe our results at D=4.\n
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\n \n\n \n \n \n \n \n \n Pre-asymptotic dynamics of the infinite size Neumann ( p = 2 spherical) model.\n \n \n \n \n\n\n \n Barbier, D.; Cugliandolo, L. F.; Lozano, G. S.; Nessi, N.; Picco, M.; and Tartaglia, A.\n\n\n \n\n\n\n Journal of Physics A: Mathematical and Theoretical, 52(45): 454002. nov 2019.\n \n\n\n\n
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@article{Barbier2019,\nabstract = {In this contribution we further study the classical disordered p=2 spherical model with Hamiltonian dynamics, or in integrable systems terms, the Neumann model, in the infinite size limit. We summarise the asymptotic results that some of us presented in a recent publication, and we deepen the analysis of the pre-asymptotic dynamics. We also discuss the possible description of the asymptotic steady state with a Generalised Gibbs Ensemble.},\narchivePrefix = {arXiv},\narxivId = {1902.06516},\nauthor = {Barbier, Damien and Cugliandolo, Leticia F. and Lozano, Gustavo S. and Nessi, Nicol{\\'{a}}s and Picco, Marco and Tartaglia, Alessandro},\ndoi = {10.1088/1751-8121/ab3ff1},\neprint = {1902.06516},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Barbier et al. - 2019 - Pre-asymptotic dynamics of the infinite size Neumann ( p = 2 spherical) model.pdf:pdf},\nissn = {1751-8113},\njournal = {Journal of Physics A: Mathematical and Theoretical},\nmonth = {nov},\nnumber = {45},\npages = {454002},\ntitle = {{Pre-asymptotic dynamics of the infinite size Neumann ( p = 2 spherical) model}},\nurl = {https://arxiv.org/abs/1902.06516 http://arxiv.org/abs/1902.06516 http://dx.doi.org/10.1088/1751-8121/ab3ff1 https://iopscience.iop.org/article/10.1088/1751-8121/ab3ff1},\nvolume = {52},\nyear = {2019}\n}\n
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\n In this contribution we further study the classical disordered p=2 spherical model with Hamiltonian dynamics, or in integrable systems terms, the Neumann model, in the infinite size limit. We summarise the asymptotic results that some of us presented in a recent publication, and we deepen the analysis of the pre-asymptotic dynamics. We also discuss the possible description of the asymptotic steady state with a Generalised Gibbs Ensemble.\n
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\n \n\n \n \n \n \n \n \n On the critical exponent $α$ of the 5D random-field Ising model.\n \n \n \n \n\n\n \n Fytas, N. G.; Martín-Mayor, V.; Parisi, G.; Picco, M.; and Sourlas, N.\n\n\n \n\n\n\n Journal of Statistical Mechanics: Theory and Experiment, 2019(9): 093203. sep 2019.\n \n\n\n\n
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@article{Fytas2019a,\nabstract = {We present a complementary estimation of the critical exponent {\\$}\\backslashalpha{\\$} of the specific heat of the 5D random-field Ising model from zero-temperature numerical simulations. Our result {\\$}\\backslashalpha = 0.12(2){\\$} is consistent with the estimation coming from the modified hyperscaling relation and provides additional evidence in favor of the recently proposed restoration of dimensional reduction in the random-field Ising model at {\\$}D = 5{\\$}.},\narchivePrefix = {arXiv},\narxivId = {1907.01340},\nauthor = {Fytas, Nikolaos G. and Mart{\\'{i}}n-Mayor, V{\\'{i}}ctor and Parisi, Giorgio and Picco, Marco and Sourlas, Nicolas},\ndoi = {10.1088/1742-5468/ab3987},\neprint = {1907.01340},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Fytas et al. - 2019 - On the critical exponent {\\$}alpha{\\$} of the 5D random-field Ising model.pdf:pdf},\nissn = {1742-5468},\njournal = {Journal of Statistical Mechanics: Theory and Experiment},\nmonth = {sep},\nnumber = {9},\npages = {093203},\ntitle = {{On the critical exponent $\\alpha$ of the 5D random-field Ising model}},\nurl = {https://arxiv.org/abs/1907.01340 http://arxiv.org/abs/1907.01340 http://dx.doi.org/10.1088/1742-5468/ab3987 https://iopscience.iop.org/article/10.1088/1742-5468/ab3987},\nvolume = {2019},\nyear = {2019}\n}\n
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\n We present a complementary estimation of the critical exponent $}\\alpha{$ of the specific heat of the 5D random-field Ising model from zero-temperature numerical simulations. Our result $}\\alpha = 0.12(2){$ is consistent with the estimation coming from the modified hyperscaling relation and provides additional evidence in favor of the recently proposed restoration of dimensional reduction in the random-field Ising model at $}D = 5{$.\n
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\n \n\n \n \n \n \n \n \n Three- and four-point connectivities of two-dimensional critical $}Q-{$ Potts random clusters on the torus.\n \n \n \n \n\n\n \n Javerzat, N.; Picco, M.; and Santachiara, R.\n\n\n \n\n\n\n Journal of Statistical Mechanics: Theory and Experiment, 2020(2): 023101. dec 2019.\n \n\n\n\n
\n\n\n\n \n \n \"Three-Paper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Javerzat2019a,\nabstract = {In a recent paper, we considered the effects of the torus lattice topology on the two-point connectivity of {\\$}Q-{\\$} Potts clusters. These effects are universal and probe non-trivial structure constants of the theory. We complete here this work by considering the torus corrections to the three- and four-point connectivities. These corrections, which depend on the scale invariant ratios of the triangle and quadrilateral formed by the three and four given points, test other non-trivial structure constants. We also present results of Monte Carlo simulations in good agreement with our predictions.},\narchivePrefix = {arXiv},\narxivId = {1912.05865},\nauthor = {Javerzat, Nina and Picco, Marco and Santachiara, Raoul},\ndoi = {10.1088/1742-5468/ab7c5e},\neprint = {1912.05865},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Javerzat, Picco, Santachiara - 2019 - Three- and four-point connectivities of two-dimensional critical {\\$}Q-{\\$} Potts random clusters on (3).pdf:pdf},\nissn = {1742-5468},\njournal = {Journal of Statistical Mechanics: Theory and Experiment},\nmonth = {dec},\nnumber = {2},\npages = {023101},\ntitle = {{Three- and four-point connectivities of two-dimensional critical {\\$}Q-{\\$} Potts random clusters on the torus}},\nurl = {https://arxiv.org/abs/1912.05865 http://dx.doi.org/10.1088/1742-5468/ab7c5e},\nvolume = {2020},\nyear = {2019}\n}\n
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\n In a recent paper, we considered the effects of the torus lattice topology on the two-point connectivity of $}Q-{$ Potts clusters. These effects are universal and probe non-trivial structure constants of the theory. We complete here this work by considering the torus corrections to the three- and four-point connectivities. These corrections, which depend on the scale invariant ratios of the triangle and quadrilateral formed by the three and four given points, test other non-trivial structure constants. We also present results of Monte Carlo simulations in good agreement with our predictions.\n
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\n \n\n \n \n \n \n \n \n Fractal character of the phase ordering kinetics of a diluted ferromagnet.\n \n \n \n \n\n\n \n Corberi, F.; Cugliandolo, L. F. L.; Insalata, F.; and Picco, M.\n\n\n \n\n\n\n Journal of Statistical Mechanics: Theory and Experiment, 2019(4): 043203. apr 2019.\n \n\n\n\n
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@article{Corberi2018,\nabstract = {We study numerically the coarsening kinetics of a two-dimensional ferromagnetic system with aleatory bond dilution. We show that interfaces between domains of opposite magnetisation are fractal on every lengthscale, but with different properties at short or long distances. Specifically, on lengthscales larger than the typical domains' size the topology is that of critical random percolation, similarly to what observed in clean systems or models with different kinds of quenched disorder. On smaller lengthscales a dilution dependent fractal dimension emerges. The Hausdorff dimension increases with increasing dilution {\\$}d{\\$} up to the value {\\$}4/3{\\$} expected at the bond percolation threshold {\\$}d=1/2{\\$}. We discuss how such different geometries develop on different lengthscales during the phase-ordering process and how their simultaneous presence determines the scaling properties of observable quantities.},\narchivePrefix = {arXiv},\narxivId = {1811.12675},\nauthor = {Corberi, Federico and Cugliandolo, Leticia F. L.F. and Insalata, Ferdinando and Picco, Marco},\ndoi = {10.1088/1742-5468/ab02ee},\neprint = {1811.12675},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Corberi et al. - 2019 - Fractal character of the phase ordering kinetics of a diluted ferromagnet.pdf:pdf},\nissn = {1742-5468},\njournal = {Journal of Statistical Mechanics: Theory and Experiment},\nkeywords = {Aging,Coarsening processes,Fractal growth,Glassy dynamics,Percolation problems,Slow relaxation},\nmonth = {apr},\nnumber = {4},\npages = {043203},\ntitle = {{Fractal character of the phase ordering kinetics of a diluted ferromagnet}},\nurl = {http://arxiv.org/abs/1811.12675 http://stacks.iop.org/1742-5468/2019/i=4/a=043203?key=crossref.0db3fc98e6f7abe91a3cc0acae4155e8},\nvolume = {2019},\nyear = {2019}\n}\n
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\n We study numerically the coarsening kinetics of a two-dimensional ferromagnetic system with aleatory bond dilution. We show that interfaces between domains of opposite magnetisation are fractal on every lengthscale, but with different properties at short or long distances. Specifically, on lengthscales larger than the typical domains' size the topology is that of critical random percolation, similarly to what observed in clean systems or models with different kinds of quenched disorder. On smaller lengthscales a dilution dependent fractal dimension emerges. The Hausdorff dimension increases with increasing dilution $}d{$ up to the value $}4/3{$ expected at the bond percolation threshold $}d=1/2{$. We discuss how such different geometries develop on different lengthscales during the phase-ordering process and how their simultaneous presence determines the scaling properties of observable quantities.\n
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\n \n\n \n \n \n \n \n \n Quenched dynamics of classical isolated systems: the spherical spin model with two-body random interactions or the Neumann integrable model.\n \n \n \n \n\n\n \n Cugliandolo, L. F.; Lozano, G. S.; Nessi, N.; Picco, M.; and Tartaglia, A.\n\n\n \n\n\n\n Journal of Statistical Mechanics: Theory and Experiment, 2018(6): 063206. jun 2018.\n \n\n\n\n
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@article{Cugliandolo2017,\nabstract = {We study the Hamiltonian dynamics of the spherical spin model with fully-connected two-body interactions drawn from a Gaussian probability distribution. In the statistical physics framework, the potential energy is of the so-called {\\$}p=2{\\$} spherical disordered kind. Most importantly for our setting, the energy conserving dynamics are equivalent to the ones of the Neumann integrable system. We take initial conditions in thermal equilibrium and we subsequently evolve the configurations with Newton dynamics dictated by a different Hamiltonian. We identify three dynamical phases depending on the parameters that characterise the initial state and the final Hamiltonian. We obtain the {\\{}$\\backslash$it global{\\}} dynamical observables with numerical and analytic methods and we show that, in most cases, they are out of thermal equilibrium. We note, however, that for shallow quenches from the condensed phase the dynamics are close to (though not at) thermal equilibrium. Surprisingly enough, for a particular relation between parameters the global observables comply Gibbs-Boltzmann equilibrium. We next set the analysis of the system with finite number of degrees of freedom in terms of {\\$}N{\\$} non-linearly coupled modes. We evaluate the mode temperatures and we relate them to the frequency-dependent effective temperature measured with the fluctuation-dissipation relation in the frequency domain, similarly to what was recently proposed for quantum integrable cases. Finally, we analyse the {\\$}N-1{\\$} integrals of motion and we use them to show that the system is out of equilibrium in all phases, even for parameters that show an apparent Gibbs-Boltzmann behaviour of global observables. We elaborate on the role played by these constants of motion in the post-quench dynamics and we briefly discuss the possible description of the asymptotic dynamics in terms of a Generalised Gibbs Ensemble.},\narchivePrefix = {arXiv},\narxivId = {1712.07688},\nauthor = {Cugliandolo, Leticia F. and Lozano, Gustavo S. and Nessi, Nicol{\\'{a}}s and Picco, Marco and Tartaglia, Alessandro},\ndoi = {10.1088/1742-5468/aac2fe},\neprint = {1712.07688},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Cugliandolo et al. - 2017 - Quenched dynamics of classical isolated systems the spherical spin model with two-body random interaction(3).pdf:pdf},\nissn = {1742-5468},\njournal = {Journal of Statistical Mechanics: Theory and Experiment},\nmonth = {jun},\nnumber = {6},\npages = {063206},\ntitle = {{Quenched dynamics of classical isolated systems: the spherical spin model with two-body random interactions or the Neumann integrable model}},\nurl = {http://arxiv.org/abs/1712.07688 http://dx.doi.org/10.1088/1742-5468/aac2fe http://stacks.iop.org/1742-5468/2018/i=6/a=063206?key=crossref.e0f528285941678c132beeabee9fbd33},\nvolume = {2018},\nyear = {2018}\n}\n
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\n We study the Hamiltonian dynamics of the spherical spin model with fully-connected two-body interactions drawn from a Gaussian probability distribution. In the statistical physics framework, the potential energy is of the so-called $}p=2{$ spherical disordered kind. Most importantly for our setting, the energy conserving dynamics are equivalent to the ones of the Neumann integrable system. We take initial conditions in thermal equilibrium and we subsequently evolve the configurations with Newton dynamics dictated by a different Hamiltonian. We identify three dynamical phases depending on the parameters that characterise the initial state and the final Hamiltonian. We obtain the \\$\\$it global\\ dynamical observables with numerical and analytic methods and we show that, in most cases, they are out of thermal equilibrium. We note, however, that for shallow quenches from the condensed phase the dynamics are close to (though not at) thermal equilibrium. Surprisingly enough, for a particular relation between parameters the global observables comply Gibbs-Boltzmann equilibrium. We next set the analysis of the system with finite number of degrees of freedom in terms of $}N{$ non-linearly coupled modes. We evaluate the mode temperatures and we relate them to the frequency-dependent effective temperature measured with the fluctuation-dissipation relation in the frequency domain, similarly to what was recently proposed for quantum integrable cases. Finally, we analyse the $}N-1{$ integrals of motion and we use them to show that the system is out of equilibrium in all phases, even for parameters that show an apparent Gibbs-Boltzmann behaviour of global observables. We elaborate on the role played by these constants of motion in the post-quench dynamics and we briefly discuss the possible description of the asymptotic dynamics in terms of a Generalised Gibbs Ensemble.\n
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\n \n\n \n \n \n \n \n \n Coarsening and percolation in the kinetic 2 d Ising model with spin exchange updates and the voter model.\n \n \n \n \n\n\n \n Tartaglia, A.; Cugliandolo, L. F.; and Picco, M.\n\n\n \n\n\n\n Journal of Statistical Mechanics: Theory and Experiment, 2018(8): 083202. aug 2018.\n \n\n\n\n
\n\n\n\n \n \n \"CoarseningPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n  \n \n 1 download\n \n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Tartaglia2018,\nabstract = {We study the early time dynamics of bimodal spin systems on {\\$}2d{\\$} lattices evolving with different microscopic stochastic updates. We treat the ferromagnetic Ising model with locally conserved order parameter (Kawasaki dynamics), the same model with globally conserved order parameter (nonlocal spin exchanges), and the voter model. As already observed for non-conserved order parameter dynamics (Glauber dynamics), in all the cases in which the stochastic dynamics satisfy detailed balance, the critical percolation state persists over a long period of time before usual coarsening of domains takes over and eventually takes the system to equilibrium. By studying the geometrical and statistical properties of time-evolving spin clusters we are able to identify a characteristic length {\\$}\\backslashell{\\_}p(t){\\$}, different from the usual length {\\$}\\backslashell{\\_}d(t) \\backslashsim t{\\^{}}{\\{}1/z{\\_}{\\{}d{\\}}{\\}}{\\$} that describes the late time coarsening, that is involved in all scaling relations in the approach to the critical percolation regime. We find that this characteristic length depends on the particular microscopic dynamics and the lattice geometry. In the case of the voter model, we observe that the system briefly passes through a critical percolation state, to later approach a dynamical regime in which the scaling behaviour of the geometrical properties of the ordered domains can be ascribed to a different criticality.},\narchivePrefix = {arXiv},\narxivId = {1805.05775},\nauthor = {Tartaglia, Alessandro and Cugliandolo, Leticia F. and Picco, Marco},\ndoi = {10.1088/1742-5468/aad366},\neprint = {1805.05775},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Tartaglia, Cugliandolo, Picco - 2018 - Coarsening and percolation in the kinetic {\\$}2d{\\$} Ising model with spin exchange updates and the vot.pdf:pdf},\nissn = {1742-5468},\njournal = {Journal of Statistical Mechanics: Theory and Experiment},\nmonth = {aug},\nnumber = {8},\npages = {083202},\ntitle = {{Coarsening and percolation in the kinetic 2 d Ising model with spin exchange updates and the voter model}},\nurl = {http://arxiv.org/abs/1805.05775 http://dx.doi.org/10.1088/1742-5468/aad366 http://stacks.iop.org/1742-5468/2018/i=8/a=083202?key=crossref.f867a517e6c7c141f8705e3ee977241e},\nvolume = {2018},\nyear = {2018}\n}\n
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\n We study the early time dynamics of bimodal spin systems on $}2d{$ lattices evolving with different microscopic stochastic updates. We treat the ferromagnetic Ising model with locally conserved order parameter (Kawasaki dynamics), the same model with globally conserved order parameter (nonlocal spin exchanges), and the voter model. As already observed for non-conserved order parameter dynamics (Glauber dynamics), in all the cases in which the stochastic dynamics satisfy detailed balance, the critical percolation state persists over a long period of time before usual coarsening of domains takes over and eventually takes the system to equilibrium. By studying the geometrical and statistical properties of time-evolving spin clusters we are able to identify a characteristic length $}\\ell{_}p(t){$, different from the usual length $}\\ell{_}d(t) \\sim t{^}{\\{}1/z{_}{\\{}d{\\}}{\\}}{$ that describes the late time coarsening, that is involved in all scaling relations in the approach to the critical percolation regime. We find that this characteristic length depends on the particular microscopic dynamics and the lattice geometry. In the case of the voter model, we observe that the system briefly passes through a critical percolation state, to later approach a dynamical regime in which the scaling behaviour of the geometrical properties of the ordered domains can be ascribed to a different criticality.\n
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\n \n\n \n \n \n \n \n \n Derivation of the spin-glass order parameter from stochastic thermodynamics.\n \n \n \n \n\n\n \n Crisanti, A.; Picco, M.; and Ritort, F.\n\n\n \n\n\n\n Physical Review E, 97(5): 052103. may 2018.\n \n\n\n\n
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@article{Crisanti2018,\nabstract = {A fluctuation relation is derived to extract the order parameter function {\\$}q(x){\\$} in weakly ergodic systems. The relation is based on measuring and classifying entropy production fluctuations according to the value of the overlap {\\$}q{\\$} between configurations. For a fixed value of {\\$}q{\\$}, entropy production fluctuations are Gaussian distributed allowing us to derive the quasi-FDT so characteristic of aging systems. The theory is validated by extracting the {\\$}q(x){\\$} in various types of glassy models. It might be generally applicable to other nonequilibrium systems and experimental small systems.},\narchivePrefix = {arXiv},\narxivId = {1805.03861},\nauthor = {Crisanti, A. and Picco, M. and Ritort, F.},\ndoi = {10.1103/PhysRevE.97.052103},\neprint = {1805.03861},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Crisanti, Picco, Ritort - 2018 - Derivation of the spin-glass order parameter from stochastic thermodynamics(2).pdf:pdf},\nissn = {2470-0045},\njournal = {Physical Review E},\nmonth = {may},\nnumber = {5},\npages = {052103},\npublisher = {American Physical Society},\ntitle = {{Derivation of the spin-glass order parameter from stochastic thermodynamics}},\nurl = {http://arxiv.org/abs/1805.03861 http://dx.doi.org/10.1103/PhysRevE.97.052103 https://link.aps.org/doi/10.1103/PhysRevE.97.052103},\nvolume = {97},\nyear = {2018}\n}\n
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\n A fluctuation relation is derived to extract the order parameter function $}q(x){$ in weakly ergodic systems. The relation is based on measuring and classifying entropy production fluctuations according to the value of the overlap $}q{$ between configurations. For a fixed value of $}q{$, entropy production fluctuations are Gaussian distributed allowing us to derive the quasi-FDT so characteristic of aging systems. The theory is validated by extracting the $}q(x){$ in various types of glassy models. It might be generally applicable to other nonequilibrium systems and experimental small systems.\n
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\n \n\n \n \n \n \n \n \n Critical percolation in the slow cooling of the bi-dimensional ferromagnetic Ising model.\n \n \n \n \n\n\n \n Ricateau, H.; Cugliandolo, L. F.; and Picco, M.\n\n\n \n\n\n\n Journal of Statistical Mechanics: Theory and Experiment, 2018(1): 013201. jan 2018.\n \n\n\n\n
\n\n\n\n \n \n \"CriticalPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n  \n \n 1 download\n \n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Ricateau2017,\nabstract = {We show that the equilibrium interfaces in the disordered phase have critical percolation fractal dimension over a wide range of length scales. We confirm that the system falls out of equilibrium at a temperature that depends on the cooling rate as predicted by the Kibble-Zurek argument and we prove that the dynamic growing length once the cooling reaches the critical point satisfies the same scaling. We determine the dynamic scaling properties of the interface winding angle variance and we show that the crossover between critical Ising and critical percolation properties is determined by the growing length reached when the system fell out of equilibrium.},\narchivePrefix = {arXiv},\narxivId = {1709.05268},\nauthor = {Ricateau, Hugo and Cugliandolo, Leticia F. and Picco, Marco},\ndoi = {10.1088/1742-5468/aa9bb4},\neprint = {1709.05268},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Ricateau, Cugliandolo, Picco - 2017 - Critical percolation in the slow cooling of the bi-dimensional ferromagnetic Ising model.pdf:pdf},\nissn = {1742-5468},\njournal = {Journal of Statistical Mechanics: Theory and Experiment},\nmonth = {jan},\nnumber = {1},\npages = {013201},\ntitle = {{Critical percolation in the slow cooling of the bi-dimensional ferromagnetic Ising model}},\nurl = {http://arxiv.org/abs/1709.05268 http://dx.doi.org/10.1088/1742-5468/aa9bb4 http://stacks.iop.org/1742-5468/2018/i=1/a=013201?key=crossref.e2295534442168e8fbc8585b3f3aa567},\nvolume = {2018},\nyear = {2018}\n}\n
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\n We show that the equilibrium interfaces in the disordered phase have critical percolation fractal dimension over a wide range of length scales. We confirm that the system falls out of equilibrium at a temperature that depends on the cooling rate as predicted by the Kibble-Zurek argument and we prove that the dynamic growing length once the cooling reaches the critical point satisfies the same scaling. We determine the dynamic scaling properties of the interface winding angle variance and we show that the crossover between critical Ising and critical percolation properties is determined by the growing length reached when the system fell out of equilibrium.\n
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\n \n\n \n \n \n \n \n \n Coarsening and percolation in the Ising Model with quenched disorder.\n \n \n \n \n\n\n \n Insalata, F.; Corberi, F.; Cugliandolo, L. F.; and Picco, M.\n\n\n \n\n\n\n Journal of Physics: Conference Series, 956(1): 012018. nov 2017.\n \n\n\n\n
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@article{Insalata2017,\nabstract = {Through large-scale numerical simulations, we study the phase ordering kinetics of the {\\$}2d{\\$} Ising Model after a zero-temperature quench from a high-temperature homogeneous initial condition. Analysing the behaviour of two important quantities -- the winding angle and the pair-connectedness -- we reveal the presence of a percolating structure in the pattern of domains. We focus on the pure case and on the random field and random bond Ising Model.},\narchivePrefix = {arXiv},\narxivId = {1711.04562},\nauthor = {Insalata, F. and Corberi, F. and Cugliandolo, L.F. F. and Picco, M.},\ndoi = {10.1088/1742-6596/956/1/012018},\neprint = {1711.04562},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Insalata et al. - 2017 - Coarsening and percolation in the Ising Model with quenched disorder(2).pdf:pdf},\nissn = {1742-6588},\njournal = {Journal of Physics: Conference Series},\nmonth = {nov},\nnumber = {1},\npages = {012018},\ntitle = {{Coarsening and percolation in the Ising Model with quenched disorder}},\nurl = {http://arxiv.org/abs/1711.04562 http://dx.doi.org/10.1088/1742-6596/956/1/012018 http://stacks.iop.org/1742-6596/956/i=1/a=012018?key=crossref.689582b6da920b4b2c9012be6bb612b9},\nvolume = {956},\nyear = {2017}\n}\n
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\n Through large-scale numerical simulations, we study the phase ordering kinetics of the $}2d{$ Ising Model after a zero-temperature quench from a high-temperature homogeneous initial condition. Analysing the behaviour of two important quantities – the winding angle and the pair-connectedness – we reveal the presence of a percolating structure in the pattern of domains. We focus on the pure case and on the random field and random bond Ising Model.\n
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\n \n\n \n \n \n \n \n \n Review of recent developments in the random-field Ising model.\n \n \n \n \n\n\n \n Fytas, N. N. G. N.; Martín-Mayor, V.; Picco, M.; Sourlas, N.; Martin-Mayor, V.; Picco, M.; Sourlas, N.; Martín-Mayor, V.; Picco, M.; and Sourlas, N.\n\n\n \n\n\n\n Journal of Statistical Physics, 172(2): 665–672. nov 2017.\n \n\n\n\n
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@article{Fytas2017,\nabstract = {A lot of progress has been made recently in our understanding of the random-field Ising model thanks to large-scale numerical simulations. In particular, it has been shown that, contrary to previous statements: the critical exponents for different probability distributions of the random fields and for diluted antiferromagnets in a field are the same. Therefore, critical universality, which is a perturbative renormalization-group prediction, holds beyond the validity regime of perturbation theory. Most notably, dimensional reduction is restored at five dimensions, i.e., the exponents of the random-field Ising model at five dimensions and those of the pure Ising ferromagnet at three dimensions are the same.},\narchivePrefix = {arXiv},\narxivId = {1711.09597},\nauthor = {Fytas, N.G. Nikolaos G. N.G. and Mart{\\'{i}}n-Mayor, V. and Picco, Marco and Sourlas, Nicolas and Martin-Mayor, Victor and Picco, Marco and Sourlas, Nicolas and Mart{\\'{i}}n-Mayor, V. and Picco, Marco and Sourlas, Nicolas},\ndoi = {10.1007/s10955-018-1955-7},\neprint = {1711.09597},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Fytas et al. - 2017 - Review of recent developments in the random-field Ising model(3).pdf:pdf},\nissn = {0022-4715},\njournal = {Journal of Statistical Physics},\nkeywords = {Disordered systems,Phase transitions,Random field Ising model},\nmonth = {nov},\nnumber = {2},\npages = {665--672},\ntitle = {{Review of recent developments in the random-field Ising model}},\nurl = {http://arxiv.org/abs/1711.09597 http://dx.doi.org/10.1007/s10955-018-1955-7 http://link.springer.com/10.1007/s10955-018-1955-7},\nvolume = {172},\nyear = {2017}\n}\n
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\n A lot of progress has been made recently in our understanding of the random-field Ising model thanks to large-scale numerical simulations. In particular, it has been shown that, contrary to previous statements: the critical exponents for different probability distributions of the random fields and for diluted antiferromagnets in a field are the same. Therefore, critical universality, which is a perturbative renormalization-group prediction, holds beyond the validity regime of perturbation theory. Most notably, dimensional reduction is restored at five dimensions, i.e., the exponents of the random-field Ising model at five dimensions and those of the pure Ising ferromagnet at three dimensions are the same.\n
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\n \n\n \n \n \n \n \n \n Critical percolation in the dynamics of the 2D ferromagnetic Ising model.\n \n \n \n \n\n\n \n Blanchard, T.; Cugliandolo, L. L. F.; Picco, M.; and Tartaglia, A.\n\n\n \n\n\n\n Journal of Statistical Mechanics: Theory and Experiment, 2017(11): 113201. nov 2017.\n \n\n\n\n
\n\n\n\n \n \n \"CriticalPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n \n \n \n \n \n \n\n\n\n
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@article{Blanchard2017,\nabstract = {We study the early time dynamics of the 2d ferromagnetic Ising model instantaneously quenched from the disordered to the ordered, low temperature, phase. We evolve the system with kinetic Monte Carlo rules that do not conserve the order parameter. We confirm the rapid approach to random critical percolation in a time-scale that diverges with the system size but is much shorter than the equilibration time. We study the scaling properties of the evolution towards critical percolation and we identify an associated growing length, different from the curvature driven one. By working with the model defined on square, triangular and honeycomb microscopic geometries we establish the dependence of this growing length on the lattice coordination. We discuss the interplay with the usual coarsening mechanism and the eventual fall into and escape from metastability.},\narchivePrefix = {arXiv},\narxivId = {1705.06508},\nauthor = {Blanchard, Thibault and Cugliandolo, L.F. Leticia F. and Picco, Marco and Tartaglia, Alessandro},\ndoi = {10.1088/1742-5468/aa9348},\neprint = {1705.06508},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Blanchard et al. - 2017 - Critical percolation in the dynamics of the 2d ferromagnetic Ising model.pdf:pdf},\nissn = {1742-5468},\njournal = {Journal of Statistical Mechanics: Theory and Experiment},\nkeywords = {Kinetic Ising models,classical Monte Carlo simulations,coarsening processes,percolation problems},\nmonth = {nov},\nnumber = {11},\npages = {113201},\ntitle = {{Critical percolation in the dynamics of the 2D ferromagnetic Ising model}},\nurl = {https://arxiv.org/abs/1705.06508 http://dx.doi.org/10.1088/1742-5468/aa9348 http://stacks.iop.org/1742-5468/2017/i=11/a=113201?key=crossref.1d0523f561407c12a7b95f091d7b9bbd},\nvolume = {2017},\nyear = {2017}\n}\n
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\n We study the early time dynamics of the 2d ferromagnetic Ising model instantaneously quenched from the disordered to the ordered, low temperature, phase. We evolve the system with kinetic Monte Carlo rules that do not conserve the order parameter. We confirm the rapid approach to random critical percolation in a time-scale that diverges with the system size but is much shorter than the equilibration time. We study the scaling properties of the evolution towards critical percolation and we identify an associated growing length, different from the curvature driven one. By working with the model defined on square, triangular and honeycomb microscopic geometries we establish the dependence of this growing length on the lattice coordination. We discuss the interplay with the usual coarsening mechanism and the eventual fall into and escape from metastability.\n
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\n \n\n \n \n \n \n \n \n Coarsening and percolation in a disordered ferromagnet.\n \n \n \n \n\n\n \n Corberi, F.; Cugliandolo, L. F.; Insalata, F.; and Picco, M.\n\n\n \n\n\n\n Physical Review E, 95(2): 022101. feb 2017.\n \n\n\n\n
\n\n\n\n \n \n \"CoarseningPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Corberi2016,\nabstract = {By studying numerically the phase-ordering kinetics of a two-dimensional ferromagnetic Ising model with quenched disorder -- either random bonds or random fields -- we show that a critical percolation structure forms in an early stage and is then progressively compactified by the ensuing coarsening process. Results are compared with the non-disordered case, where a similar phenomenon is observed, and interpreted within a dynamical scaling framework.},\narchivePrefix = {arXiv},\narxivId = {1611.04828},\nauthor = {Corberi, Federico and Cugliandolo, Leticia F. and Insalata, Ferdinando and Picco, Marco},\ndoi = {10.1103/PhysRevE.95.022101},\neprint = {1611.04828},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Corberi et al. - 2016 - Coarsening and percolation in a disordered ferromagnet.pdf:pdf},\nissn = {2470-0045},\njournal = {Physical Review E},\nmonth = {feb},\nnumber = {2},\npages = {022101},\ntitle = {{Coarsening and percolation in a disordered ferromagnet}},\nurl = {http://arxiv.org/abs/1611.04828 http://dx.doi.org/10.1103/PhysRevE.95.022101 https://link.aps.org/doi/10.1103/PhysRevE.95.022101},\nvolume = {95},\nyear = {2017}\n}\n
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\n By studying numerically the phase-ordering kinetics of a two-dimensional ferromagnetic Ising model with quenched disorder – either random bonds or random fields – we show that a critical percolation structure forms in an early stage and is then progressively compactified by the ensuing coarsening process. Results are compared with the non-disordered case, where a similar phenomenon is observed, and interpreted within a dynamical scaling framework.\n
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\n \n\n \n \n \n \n \n \n Specific-heat exponent and modified hyperscaling in the 4D random-field Ising model.\n \n \n \n \n\n\n \n Fytas, N. G.; Martín-Mayor, V.; Picco, M.; and Sourlas, N.\n\n\n \n\n\n\n Journal of Statistical Mechanics: Theory and Experiment, 2017(3): 033302. mar 2017.\n \n\n\n\n
\n\n\n\n \n \n \"Specific-heatPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n \n \n \n \n\n\n\n
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@article{Fytas2016a,\nabstract = {We report a high-precision numerical estimation of the critical exponent {\\$}\\backslashalpha{\\$} of the specific heat of the random-field Ising model in four dimensions. Our result {\\$}\\backslashalpha = 0.12(1){\\$} indicates a diverging specific-heat behavior and is consistent with the estimation coming from the modified hyperscaling relation using our estimate of {\\$}\\backslashtheta{\\$} via the anomalous dimensions {\\$}\\backslasheta{\\$} and {\\$}\\backslashbar{\\{}\\backslasheta{\\}}{\\$}. Our analysis benefited form a high-statistics zero-temperature numerical simulation of the model for two distributions of the random fields, namely a Gaussian and Poissonian distribution, as well as recent advances in finite-size scaling and reweighting methods for disordered systems. An original estimate of the critical slowing down exponent {\\$}z{\\$} of the maximum-flow algorithm used is also provided.},\narchivePrefix = {arXiv},\narxivId = {1611.09015},\nauthor = {Fytas, N.G. G. and Mart{\\'{i}}n-Mayor, V. and Picco, M. and Sourlas, N.},\ndoi = {10.1088/1742-5468/aa5dc3},\neprint = {1611.09015},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Fytas et al. - 2016 - Specific-heat exponent and modified hyperscaling in the 4D random-field Ising model.pdf:pdf},\nissn = {1742-5468},\njournal = {Journal of Statistical Mechanics: Theory and Experiment},\nkeywords = {critical exponents and amplitudes,finite-size scaling,numerical simulations},\nmonth = {mar},\nnumber = {3},\npages = {033302},\ntitle = {{Specific-heat exponent and modified hyperscaling in the 4D random-field Ising model}},\nurl = {http://arxiv.org/abs/1611.09015 http://dx.doi.org/10.1088/1742-5468/aa5dc3 http://stacks.iop.org/1742-5468/2017/i=3/a=033302?key=crossref.2552d3aeac7d8d89add3a06895f23a08},\nvolume = {2017},\nyear = {2017}\n}\n
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\n We report a high-precision numerical estimation of the critical exponent $}\\alpha{$ of the specific heat of the random-field Ising model in four dimensions. Our result $}\\alpha = 0.12(1){$ indicates a diverging specific-heat behavior and is consistent with the estimation coming from the modified hyperscaling relation using our estimate of $}\\theta{$ via the anomalous dimensions $}\\eta{$ and $}\\̄{}\\eta{\\}}{$. Our analysis benefited form a high-statistics zero-temperature numerical simulation of the model for two distributions of the random fields, namely a Gaussian and Poissonian distribution, as well as recent advances in finite-size scaling and reweighting methods for disordered systems. An original estimate of the critical slowing down exponent $}z{$ of the maximum-flow algorithm used is also provided.\n
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\n \n\n \n \n \n \n \n \n Restoration of dimensional reduction in the random-field Ising model at five dimensions.\n \n \n \n \n\n\n \n Fytas, N. G.; Martín-Mayor, V.; Picco, M.; and Sourlas, N.\n\n\n \n\n\n\n Physical Review E, 95(4): 042117. apr 2017.\n \n\n\n\n
\n\n\n\n \n \n \"RestorationPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
\n
@article{Fytas2016d,\nabstract = {The random-field Ising model is one of the few disordered systems where the perturbative renormalization group can be carried out to all orders of perturbation theory. This analysis predicts dimensional reduction, i.e., that the critical properties of the random-field Ising model in {\\$}D{\\$} dimensions are identical to those of the pure Ising ferromagnet in {\\$}D-2{\\$} dimensions. It is well known that dimensional reduction is not true in three dimensions, thus invalidating the perturbative renormalization group prediction. Here, we report high-precision numerical simulations of the 5D random-field Ising model at zero temperature. We illustrate universality by comparing different probability distributions for the random fields. We compute all the relevant critical exponents (including the critical slowing down exponent for the ground-state finding algorithm), as well as several other renormalization-group invariants. The estimated values of the critical exponents of the 5D random-field Ising model are statistically compatible to those of the pure 3D Ising ferromagnet. These results support the restoration of dimensional reduction at {\\$}D = 5{\\$}. We thus conclude that the failure of the perturbative renormalization group is a low-dimensional phenomenon. We close our contribution by comparing universal quantities for the random-field problem at dimensions {\\$}3 \\backslashleq D {\\textless} 6{\\$} to their values in the pure Ising model at {\\$}D-2{\\$} dimensions and we provide a clear verification of the Rushbrooke equality at all studied dimensions.},\narchivePrefix = {arXiv},\narxivId = {1612.06156},\nauthor = {Fytas, Nikolaos G. and Mart{\\'{i}}n-Mayor, V{\\'{i}}ctor and Picco, Marco and Sourlas, Nicolas},\ndoi = {10.1103/PhysRevE.95.042117},\neprint = {1612.06156},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Fytas et al. - 2017 - Restoration of dimensional reduction in the random-field Ising model at five dimensions.pdf:pdf},\nissn = {2470-0045},\njournal = {Physical Review E},\nmonth = {apr},\nnumber = {4},\npages = {042117},\ntitle = {{Restoration of dimensional reduction in the random-field Ising model at five dimensions}},\nurl = {http://arxiv.org/abs/1612.06156 http://dx.doi.org/10.1103/PhysRevE.95.042117 http://link.aps.org/doi/10.1103/PhysRevE.95.042117},\nvolume = {95},\nyear = {2017}\n}\n
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\n The random-field Ising model is one of the few disordered systems where the perturbative renormalization group can be carried out to all orders of perturbation theory. This analysis predicts dimensional reduction, i.e., that the critical properties of the random-field Ising model in $}D{$ dimensions are identical to those of the pure Ising ferromagnet in $}D-2{$ dimensions. It is well known that dimensional reduction is not true in three dimensions, thus invalidating the perturbative renormalization group prediction. Here, we report high-precision numerical simulations of the 5D random-field Ising model at zero temperature. We illustrate universality by comparing different probability distributions for the random fields. We compute all the relevant critical exponents (including the critical slowing down exponent for the ground-state finding algorithm), as well as several other renormalization-group invariants. The estimated values of the critical exponents of the 5D random-field Ising model are statistically compatible to those of the pure 3D Ising ferromagnet. These results support the restoration of dimensional reduction at $}D = 5{$. We thus conclude that the failure of the perturbative renormalization group is a low-dimensional phenomenon. We close our contribution by comparing universal quantities for the random-field problem at dimensions $}3 \\leq D {\\textless} 6{$ to their values in the pure Ising model at $}D-2{$ dimensions and we provide a clear verification of the Rushbrooke equality at all studied dimensions.\n
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\n  \n 2016\n \n \n (3)\n \n \n
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\n \n\n \n \n \n \n \n \n Phase Transitions in Disordered Systems: The Example of the Random-Field Ising Model in Four Dimensions.\n \n \n \n \n\n\n \n Fytas, N. G.; Martín-Mayor, V.; Picco, M.; and Sourlas, N.\n\n\n \n\n\n\n Physical Review Letters, 116(22): 227201. jun 2016.\n \n\n\n\n
\n\n\n\n \n \n \"PhasePaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
\n
@article{Fytas2016c,\nabstract = {By performing a high-statistics simulation of the {\\$}D=4{\\$} random-field Ising model at zero temperature for different shapes of the random-field distribution, we show that the model is ruled by a single universality class. We compute to a high accuracy the complete set of critical exponents for this class, including the correction-to-scaling exponent. Our results indicate that in four dimensions: (i) dimensional reduction as predicted by the perturbative renormalization group does not hold and (ii) three independent critical exponents are needed to described the transition.},\narchivePrefix = {arXiv},\narxivId = {1605.05072},\nauthor = {Fytas, Nikolaos G. and Mart{\\'{i}}n-Mayor, V{\\'{i}}ctor and Picco, Marco and Sourlas, Nicolas},\ndoi = {10.1103/PhysRevLett.116.227201},\neprint = {1605.05072},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Fytas et al. - 2016 - Phase transitions in disordered systems the example of the random-field Ising model in four dimensions(2).pdf:pdf;:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Fytas et al. - 2016 - Phase Transitions in Disordered Systems The Example of the Random-Field Ising Model in Four Dimensions(3).pdf:pdf},\nissn = {0031-9007},\njournal = {Physical Review Letters},\nmonth = {jun},\nnumber = {22},\npages = {227201},\ntitle = {{Phase Transitions in Disordered Systems: The Example of the Random-Field Ising Model in Four Dimensions}},\nurl = {http://arxiv.org/abs/1605.05072 http://dx.doi.org/10.1103/PhysRevLett.116.227201 http://link.aps.org/doi/10.1103/PhysRevLett.116.227201},\nvolume = {116},\nyear = {2016}\n}\n
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\n\n\n
\n By performing a high-statistics simulation of the $}D=4{$ random-field Ising model at zero temperature for different shapes of the random-field distribution, we show that the model is ruled by a single universality class. We compute to a high accuracy the complete set of critical exponents for this class, including the correction-to-scaling exponent. Our results indicate that in four dimensions: (i) dimensional reduction as predicted by the perturbative renormalization group does not hold and (ii) three independent critical exponents are needed to described the transition.\n
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\n \n\n \n \n \n \n \n \n Phase separation and critical percolation in bidimensional spin-exchange models.\n \n \n \n \n\n\n \n Tartaglia, A.; Cugliandolo, L. F.; and Picco, M.\n\n\n \n\n\n\n EPL (Europhysics Letters), 116(2): 26001. oct 2016.\n \n\n\n\n
\n\n\n\n \n \n \"PhasePaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Tartaglia2016,\nabstract = {Binary mixtures prepared in an homogeneous phase and quenched into a two-phase region phase-separate via a coarsening process whereby domains of the two phases grow in time. With a numerical study of a spin-exchange model we show that this dynamics first takes a system with equal density of the two species to a critical percolation state. We prove this claim and we determine the time-dependence of the growing length associated to this process with the scaling analysis of the statistical and morphological properties of the clusters of the two phases.},\narchivePrefix = {arXiv},\narxivId = {1607.04067},\nauthor = {Tartaglia, Alessandro and Cugliandolo, Leticia F. and Picco, Marco},\ndoi = {10.1209/0295-5075/116/26001},\neprint = {1607.04067},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Tartaglia, Cugliandolo, Picco - 2016 - Phase separation and critical percolation in bidimensional spin-exchange models.pdf:pdf},\nissn = {0295-5075},\njournal = {EPL (Europhysics Letters)},\nmonth = {oct},\nnumber = {2},\npages = {26001},\ntitle = {{Phase separation and critical percolation in bidimensional spin-exchange models}},\nurl = {http://arxiv.org/abs/1607.04067 http://dx.doi.org/10.1209/0295-5075/116/26001 http://stacks.iop.org/0295-5075/116/i=2/a=26001?key=crossref.72f5622fac4646a021a44ef95ef40bbb},\nvolume = {116},\nyear = {2016}\n}\n
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\n Binary mixtures prepared in an homogeneous phase and quenched into a two-phase region phase-separate via a coarsening process whereby domains of the two phases grow in time. With a numerical study of a spin-exchange model we show that this dynamics first takes a system with equal density of the two species to a critical percolation state. We prove this claim and we determine the time-dependence of the growing length associated to this process with the scaling analysis of the statistical and morphological properties of the clusters of the two phases.\n
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\n \n\n \n \n \n \n \n \n A conformal bootstrap approach to critical percolation in two dimensions.\n \n \n \n \n\n\n \n Picco, M.; Ribault, S.; and Santachiara, R.\n\n\n \n\n\n\n SciPost Physics, 1(1): 13. jul 2016.\n \n\n\n\n
\n\n\n\n \n \n \"APaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Picco2016,\nabstract = {We study four-point functions of critical percolation in two dimensions, and more generally of the Potts model. We propose an exact ansatz for the spectrum: an infinite, discrete and non-diagonal combination of representations of the Virasoro algebra. Based on this ansatz, we compute four-point functions using a numerical conformal bootstrap approach. The results agree with Monte-Carlo computations of connectivities of random clusters.},\narchivePrefix = {arXiv},\narxivId = {1607.07224},\nauthor = {Picco, Marco and Ribault, Sylvain and Santachiara, Raoul},\ndoi = {10.21468/SciPostPhys.1.1.009},\neprint = {1607.07224},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Picco, Ribault, Santachiara - 2016 - A conformal bootstrap approach to critical percolation in two dimensions(2).pdf:pdf;:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Picco, Ribault, Santachiara - 2016 - A conformal bootstrap approach to critical percolation in two dimensions(4).pdf:pdf},\nissn = {2542-4653},\njournal = {SciPost Physics},\nmonth = {jul},\nnumber = {1},\npages = {13},\ntitle = {{A conformal bootstrap approach to critical percolation in two dimensions}},\nurl = {http://arxiv.org/abs/1607.07224 http://dx.doi.org/10.21468/SciPostPhys.1.1.009 https://scipost.org/10.21468/SciPostPhys.1.1.009},\nvolume = {1},\nyear = {2016}\n}\n
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\n We study four-point functions of critical percolation in two dimensions, and more generally of the Potts model. We propose an exact ansatz for the spectrum: an infinite, discrete and non-diagonal combination of representations of the Virasoro algebra. Based on this ansatz, we compute four-point functions using a numerical conformal bootstrap approach. The results agree with Monte-Carlo computations of connectivities of random clusters.\n
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\n  \n 2015\n \n \n (3)\n \n \n
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\n \n\n \n \n \n \n \n \n Slicing the three-dimensional Ising model: Critical equilibrium and coarsening dynamics.\n \n \n \n \n\n\n \n Arenzon, J. J.; Cugliandolo, L. F.; and Picco, M.\n\n\n \n\n\n\n Physical Review E, 91(3): 032142. mar 2015.\n \n\n\n\n
\n\n\n\n \n \n \"SlicingPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Arenzon2015,\nabstract = {We study the evolution of spin clusters on two dimensional slices of the {\\$}3d{\\$} Ising model in contact with a heat bath after a sudden quench to a subcritical temperature. We analyze the evolution of some simple initial configurations, such as a sphere and a torus, of one phase embedded into the other, to confirm that their area disappears linearly in time and to establish the temperature dependence of the prefactor in each case. Two generic kinds of initial states are later used: equilibrium configurations either at infinite temperature or at the paramagnetic-ferromagnetic phase transition. We investigate the morphological domain structure of the coarsening configurations on {\\$}2d{\\$} slices of the {\\$}3d{\\$} system, comparing with the behavior of the bidimensional model.},\narchivePrefix = {arXiv},\narxivId = {1412.7456},\nauthor = {Arenzon, Jeferson J. and Cugliandolo, Leticia F. and Picco, Marco},\ndoi = {10.1103/PhysRevE.91.032142},\neprint = {1412.7456},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Arenzon, Cugliandolo, Picco - 2014 - Slicing the three-dimensional Ising model Critical equilibrium and coarsening dynamics.pdf:pdf},\nissn = {1539-3755},\njournal = {Physical Review E},\nmonth = {mar},\nnumber = {3},\npages = {032142},\ntitle = {{Slicing the three-dimensional Ising model: Critical equilibrium and coarsening dynamics}},\nurl = {http://arxiv.org/abs/1412.7456 http://link.aps.org/doi/10.1103/PhysRevE.91.032142},\nvolume = {91},\nyear = {2015}\n}\n
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\n We study the evolution of spin clusters on two dimensional slices of the $}3d{$ Ising model in contact with a heat bath after a sudden quench to a subcritical temperature. We analyze the evolution of some simple initial configurations, such as a sphere and a torus, of one phase embedded into the other, to confirm that their area disappears linearly in time and to establish the temperature dependence of the prefactor in each case. Two generic kinds of initial states are later used: equilibrium configurations either at infinite temperature or at the paramagnetic-ferromagnetic phase transition. We investigate the morphological domain structure of the coarsening configurations on $}2d{$ slices of the $}3d{$ system, comparing with the behavior of the bidimensional model.\n
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\n \n\n \n \n \n \n \n \n Percolation and coarsening in the bidimensional voter model.\n \n \n \n \n\n\n \n Tartaglia, A.; Cugliandolo, L. L. F; and Picco, M.\n\n\n \n\n\n\n Physical Review E, 92(4): 042109. oct 2015.\n \n\n\n\n
\n\n\n\n \n \n \"PercolationPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Tartaglia2015,\nabstract = {We study the bidimensional voter model on a square lattice with numerical simulations. We demonstrate that the evolution takes place in two distinct dynamic regimes; a first approach towards critical site percolation and a further approach towards full consensus. We calculate the time dependence of the two growing lengths, finding that they are both algebraic but with different exponents (apart from possible logarithmic corrections). We analyze the morphology and statistics of clusters of voters with the same opinion. We compare these results to the ones for curvature driven two-dimensional coarsening.},\narchivePrefix = {arXiv},\narxivId = {1506.05321},\nauthor = {Tartaglia, Alessandro and Cugliandolo, L.F. Leticia F and Picco, Marco},\ndoi = {10.1103/PhysRevE.92.042109},\neprint = {1506.05321},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Tartaglia, Cugliandolo, Picco - 2015 - Percolation and coarsening in the bidimensional voter model(2).pdf:pdf},\nissn = {1539-3755},\njournal = {Physical Review E},\nmonth = {oct},\nnumber = {4},\npages = {042109},\npmid = {26565170},\ntitle = {{Percolation and coarsening in the bidimensional voter model}},\nurl = {http://arxiv.org/abs/1506.05321 https://link.aps.org/doi/10.1103/PhysRevE.92.042109},\nvolume = {92},\nyear = {2015}\n}\n
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\n We study the bidimensional voter model on a square lattice with numerical simulations. We demonstrate that the evolution takes place in two distinct dynamic regimes; a first approach towards critical site percolation and a further approach towards full consensus. We calculate the time dependence of the two growing lengths, finding that they are both algebraic but with different exponents (apart from possible logarithmic corrections). We analyze the morphology and statistics of clusters of voters with the same opinion. We compare these results to the ones for curvature driven two-dimensional coarsening.\n
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\n \n\n \n \n \n \n \n \n Diluted antiferromagnetic 3D Ising model in a field.\n \n \n \n \n\n\n \n Picco, M.; and Sourlas, N.\n\n\n \n\n\n\n EPL (Europhysics Letters), 109(3): 37001. feb 2015.\n \n\n\n\n
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@article{Picco2015,\nabstract = {{\\textcopyright} CopyrightEPLA, 2015. We present numerical simulations for the diluted antiferromagnetic 3D Ising model in an external magnetic field (DAFF) at zero temperature. Our results are compatible with the DAFF being in the same universality class as the random field Ising model, in agreement with the renormalization group prediction.},\nauthor = {Picco, Marco and Sourlas, Nicolas},\ndoi = {10.1209/0295-5075/109/37001},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Picco, Sourlas - 2015 - Diluted antiferromagnetic 3D Ising model in a field.pdf:pdf},\nissn = {0295-5075},\njournal = {EPL (Europhysics Letters)},\nmonth = {feb},\nnumber = {3},\npages = {37001},\ntitle = {{Diluted antiferromagnetic 3D Ising model in a field}},\nurl = {http://stacks.iop.org/0295-5075/109/i=3/a=37001?key=crossref.a43813d4118ce4ac798577910fa89d04},\nvolume = {109},\nyear = {2015}\n}\n
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\n © CopyrightEPLA, 2015. We present numerical simulations for the diluted antiferromagnetic 3D Ising model in an external magnetic field (DAFF) at zero temperature. Our results are compatible with the DAFF being in the same universality class as the random field Ising model, in agreement with the renormalization group prediction.\n
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\n  \n 2014\n \n \n (2)\n \n \n
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\n \n\n \n \n \n \n \n \n How soon after a zero-temperature quench is the fate of the Ising model sealed?.\n \n \n \n \n\n\n \n Blanchard, T.; Corberi, F.; Cugliandolo, L. F.; and Picco, M.\n\n\n \n\n\n\n EPL (Europhysics Letters), 106(6): 66001. dec 2014.\n \n\n\n\n
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@article{Blanchard2014,\nabstract = {We study the transient between a fully disordered initial condition and a percolating structure in the low-temperature non-conserved order parameter dynamics of the bi-dimensional Ising model. We show that a stable structure of spanning clusters establishes at a time {\\$}t{\\_}p \\backslashsimeq L{\\^{}}{\\{}\\backslashalpha{\\_}p{\\}}{\\$}. Our numerical results yield {\\$}\\backslashalpha{\\_}p=0.50(2){\\$} for the square and kagome, {\\$}\\backslashalpha{\\_}p=0.33(2){\\$} for the triangular and {\\$}\\backslashalpha{\\_}p=0.38(5){\\$} for the bowtie-a lattices.We generalise the dynamic scaling hypothesis to take into account this new time-scale. We discuss the implications of these results for other non-equilibrium processes.},\narchivePrefix = {arXiv},\narxivId = {1312.1712},\nauthor = {Blanchard, Thibault and Corberi, F. and Cugliandolo, Leticia F. and Picco, Marco},\ndoi = {10.1209/0295-5075/106/66001},\neprint = {1312.1712},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Blanchard, Cugliandolo, Picco - 2013 - How soon after a zero-temperature quench is the fate of the Ising model sealed(2).pdf:pdf},\nissn = {0295-5075},\njournal = {EPL (Europhysics Letters)},\nmonth = {dec},\nnumber = {6},\npages = {66001},\ntitle = {{How soon after a zero-temperature quench is the fate of the Ising model sealed?}},\nurl = {http://arxiv.org/abs/1312.1712 http://stacks.iop.org/0295-5075/106/i=6/a=66001?key=crossref.6897442746f4314f77925c48b9e50e1d},\nvolume = {106},\nyear = {2014}\n}\n
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\n We study the transient between a fully disordered initial condition and a percolating structure in the low-temperature non-conserved order parameter dynamics of the bi-dimensional Ising model. We show that a stable structure of spanning clusters establishes at a time $}t{_}p \\simeq L{^}{\\{}\\alpha{_}p{\\}}{$. Our numerical results yield $}\\alpha{_}p=0.50(2){$ for the square and kagome, $}\\alpha{_}p=0.33(2){$ for the triangular and $}\\alpha{_}p=0.38(5){$ for the bowtie-a lattices.We generalise the dynamic scaling hypothesis to take into account this new time-scale. We discuss the implications of these results for other non-equilibrium processes.\n
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\n \n\n \n \n \n \n \n \n Persistence in the two dimensional ferromagnetic Ising model.\n \n \n \n \n\n\n \n Blanchard, T.; Cugliandolo, L. F.; and Picco, M.\n\n\n \n\n\n\n Journal of Statistical Mechanics: Theory and Experiment, 2014(12): P12021. dec 2014.\n \n\n\n\n
\n\n\n\n \n \n \"PersistencePaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Blanchard2014a,\nabstract = {We present very accurate numerical estimates of the time and size dependence of the zero-temperature local persistence in the {\\$}2d{\\$} ferromagnetic Ising model. We show that the effective exponent decays algebraically to an asymptotic value {\\$}\\backslashtheta{\\$} that depends upon the initial condition. More precisely, we find that {\\$}\\backslashtheta{\\$} takes one universal value {\\$}0.199(2){\\$} for initial conditions with short-range spatial correlations as in a paramagnetic state, and the value {\\$}0.033(1){\\$} for initial conditions with the long-range spatial correlations of the critical Ising state. We checked universality by working with a square and a triangular lattice, and by imposing free and periodic boundary conditions. We found that the effective exponent suffers from stronger finite size effects in the former case.},\narchivePrefix = {arXiv},\narxivId = {1410.4007},\nauthor = {Blanchard, Thibault and Cugliandolo, Leticia F. and Picco, Marco},\ndoi = {10.1088/1742-5468/2014/12/P12021},\neprint = {1410.4007},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Blanchard, Cugliandolo, Picco - 2014 - Persistence in the two dimensional ferromagnetic Ising model.pdf:pdf},\nissn = {1742-5468},\njournal = {Journal of Statistical Mechanics: Theory and Experiment},\nmonth = {dec},\nnumber = {12},\npages = {P12021},\ntitle = {{Persistence in the two dimensional ferromagnetic Ising model}},\nurl = {http://arxiv.org/abs/1410.4007v1 http://dx.doi.org/10.1088/1742-5468/2014/12/P12021 http://stacks.iop.org/1742-5468/2014/i=12/a=P12021?key=crossref.46336e080945eb8ec98e4c99c7826d2e},\nvolume = {2014},\nyear = {2014}\n}\n
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\n We present very accurate numerical estimates of the time and size dependence of the zero-temperature local persistence in the $}2d{$ ferromagnetic Ising model. We show that the effective exponent decays algebraically to an asymptotic value $}\\theta{$ that depends upon the initial condition. More precisely, we find that $}\\theta{$ takes one universal value $}0.199(2){$ for initial conditions with short-range spatial correlations as in a paramagnetic state, and the value $}0.033(1){$ for initial conditions with the long-range spatial correlations of the critical Ising state. We checked universality by working with a square and a triangular lattice, and by imposing free and periodic boundary conditions. We found that the effective exponent suffers from stronger finite size effects in the former case.\n
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\n \n\n \n \n \n \n \n \n Spin clusters and conformal field theory.\n \n \n \n \n\n\n \n Delfino, G.; Picco, M.; Santachiara, R.; and Viti, J.\n\n\n \n\n\n\n Journal of Statistical Mechanics: Theory and Experiment, 2013(11): P11011. nov 2013.\n \n\n\n\n
\n\n\n\n \n \n \"SpinPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n \n \n \n \n\n\n\n
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@article{Delfino2013,\nabstract = {We study numerically the fractal dimensions and the bulk three-point connectivity for the spin clusters of the Q-state Potts model in two dimensions with {\\$}1\\backslashleq Q\\backslashleq 4{\\$}. We check that the usually invoked correspondence between FK clusters and spin clusters works at the level of fractal dimensions. However, the fine structure of the conformal field theories describing critical clusters first manifests at the level of the three-point connectivities. Contrary to what recently found for FK clusters, no obvious relation emerges for generic Q between the spin cluster connectivity and the structure constants obtained from analytic continuation of the minimal model ones. The numerical results strongly suggest then that spin and FK clusters are described by conformal field theories with different realizations of the color symmetry of the Potts model.},\narchivePrefix = {arXiv},\narxivId = {arXiv:1307.6123v2},\nauthor = {Delfino, Gesualdo and Picco, Marco and Santachiara, R. and Viti, J.},\ndoi = {10.1088/1742-5468/2013/11/P11011},\neprint = {arXiv:1307.6123v2},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Delfino et al. - 2013 - Spin clusters and conformal field theory(2).pdf:pdf},\nisbn = {9789048128105},\nissn = {1742-5468},\njournal = {Journal of Statistical Mechanics: Theory and Experiment},\nkeywords = {classical Monte Carlo simulations,critical exponents and amplitudes (theory),renormalization group},\nmonth = {nov},\nnumber = {11},\npages = {P11011},\ntitle = {{Spin clusters and conformal field theory}},\nurl = {http://arxiv.org/abs/1307.6123 http://iopscience.iop.org/1742-5468/2013/11/P11011 http://stacks.iop.org/1742-5468/2013/i=11/a=P11011?key=crossref.449383021b215981e2799981bb8a8322},\nvolume = {2013},\nyear = {2013}\n}\n
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\n We study numerically the fractal dimensions and the bulk three-point connectivity for the spin clusters of the Q-state Potts model in two dimensions with $}1\\leq Q\\leq 4{$. We check that the usually invoked correspondence between FK clusters and spin clusters works at the level of fractal dimensions. However, the fine structure of the conformal field theories describing critical clusters first manifests at the level of the three-point connectivities. Contrary to what recently found for FK clusters, no obvious relation emerges for generic Q between the spin cluster connectivity and the structure constants obtained from analytic continuation of the minimal model ones. The numerical results strongly suggest then that spin and FK clusters are described by conformal field theories with different realizations of the color symmetry of the Potts model.\n
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\n \n\n \n \n \n \n \n \n Influence of long-range interactions on the critical behavior of the Ising model.\n \n \n \n \n\n\n \n Blanchard, T.; Picco, M.; and Rajabpour, M. A.\n\n\n \n\n\n\n EPL (Europhysics Letters), 101(5): 56003. mar 2013.\n \n\n\n\n
\n\n\n\n \n \n \"InfluencePaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n  \n \n 1 download\n \n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Blanchard2013,\nabstract = {We study the ferromagnetic Ising model with long-range interactions in two dimensions. We first present results of a Monte Carlo study which shows that the long-range interactions dominate over the short-range ones in the intermediate regime of interaction range. Based on a renormalization group analysis, we propose a way of computing the influence of the long-range interactions as a dimensional change.},\narchivePrefix = {arXiv},\narxivId = {1211.6758},\nauthor = {Blanchard, Thibault and Picco, Marco and Rajabpour, M.A. A.},\ndoi = {10.1209/0295-5075/101/56003},\neprint = {1211.6758},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Blanchard, Picco, Rajabpour - 2012 - Influence of long-range interactions on the critical behavior of the Ising model(2).pdf:pdf},\nissn = {0295-5075},\njournal = {EPL (Europhysics Letters)},\nlanguage = {en},\nmonth = {mar},\nnumber = {5},\npages = {56003},\npublisher = {IOP Publishing},\ntitle = {{Influence of long-range interactions on the critical behavior of the Ising model}},\nurl = {http://iopscience.iop.org/0295-5075/101/5/56003/article/ http://arxiv.org/abs/1211.6758 http://stacks.iop.org/0295-5075/101/i=5/a=56003?key=crossref.5bc43365376b2590e451272be02aa97b},\nvolume = {101},\nyear = {2013}\n}\n
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\n We study the ferromagnetic Ising model with long-range interactions in two dimensions. We first present results of a Monte Carlo study which shows that the long-range interactions dominate over the short-range ones in the intermediate regime of interaction range. Based on a renormalization group analysis, we propose a way of computing the influence of the long-range interactions as a dimensional change.\n
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\n \n\n \n \n \n \n \n \n On the phase transition of the 3D random field Ising model.\n \n \n \n \n\n\n \n Picco, M.; and Sourlas, N.\n\n\n \n\n\n\n Journal of Statistical Mechanics: Theory and Experiment, 2014(3): P03019. oct 2013.\n \n\n\n\n
\n\n\n\n \n \n \"OnPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Picco2013a,\nabstract = {We present numerical simulations of the random field Ising model in three dimensions at zero temperature. The critical exponents are found to agree with previous results. We argue that the ground state magnetisation at the critical point is different from zero and its derivative with respect to the ferromagnetic coupling diverges as L{\\^{}}{\\{}1/nu{\\}} where L is the linear size of the system and nu is the correlation length exponent. The critical amplitude ratio of the magnetic susceptibilities is very large, equal to 233.1 +/- 1.5. We found strong sample to sample fluctuations which obey finite size scaling. The probability distribution of the size of small energy excitations is maximally non self averaging and obeys finite size scaling.},\narchivePrefix = {arXiv},\narxivId = {1310.2364},\nauthor = {Picco, Marco and Sourlas, Nicolas},\ndoi = {10.1088/1742-5468/2014/03/P03019},\neprint = {1310.2364},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Picco, Sourlas - 2014 - On the phase transition of the 3D random field Ising model.pdf:pdf},\nissn = {1742-5468},\njournal = {Journal of Statistical Mechanics: Theory and Experiment},\nlanguage = {en},\nmonth = {oct},\nnumber = {3},\npages = {P03019},\npublisher = {IOP Publishing},\ntitle = {{On the phase transition of the 3D random field Ising model}},\nurl = {http://arxiv.org/abs/1310.2364 http://iopscience.iop.org/1742-5468/2014/3/P03019/article/},\nvolume = {2014},\nyear = {2013}\n}\n
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\n We present numerical simulations of the random field Ising model in three dimensions at zero temperature. The critical exponents are found to agree with previous results. We argue that the ground state magnetisation at the critical point is different from zero and its derivative with respect to the ferromagnetic coupling diverges as L^\\1/nu\\ where L is the linear size of the system and nu is the correlation length exponent. The critical amplitude ratio of the magnetic susceptibilities is very large, equal to 233.1 +/- 1.5. We found strong sample to sample fluctuations which obey finite size scaling. The probability distribution of the size of small energy excitations is maximally non self averaging and obeys finite size scaling.\n
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\n \n\n \n \n \n \n \n \n Fluctuation Relation for Weakly Ergodic Aging Systems.\n \n \n \n \n\n\n \n Crisanti, A.; Picco, M.; and Ritort, F.\n\n\n \n\n\n\n Physical Review Letters, 110(8): 080601. feb 2013.\n \n\n\n\n
\n\n\n\n \n \n \"FluctuationPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Crisanti2013,\nabstract = {A fluctuation relation for aging systems is introduced and verified by extensive numerical simulations. It is based on the hypothesis of partial equilibration over phase-space regions in a scenario of entropy-driven relaxation. The relation provides a simple alternative method, amenable of experimental implementation, to measure replica symmetry breaking parameters in aging systems. The connection with the effective temperatures obtained from the fluctuation-dissipation theorem is discussed.},\nauthor = {Crisanti, A. and Picco, M. and Ritort, F.},\ndoi = {10.1103/PhysRevLett.110.080601},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Crisanti, Picco, Ritort - 2013 - Fluctuation Relation for Weakly Ergodic Aging Systems.pdf:pdf},\nissn = {0031-9007},\njournal = {Physical Review Letters},\nmonth = {feb},\nnumber = {8},\npages = {080601},\npublisher = {American Physical Society},\nshorttitle = {Phys. Rev. Lett.},\ntitle = {{Fluctuation Relation for Weakly Ergodic Aging Systems}},\nurl = {http://link.aps.org/doi/10.1103/PhysRevLett.110.080601},\nvolume = {110},\nyear = {2013}\n}\n
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\n A fluctuation relation for aging systems is introduced and verified by extensive numerical simulations. It is based on the hypothesis of partial equilibration over phase-space regions in a scenario of entropy-driven relaxation. The relation provides a simple alternative method, amenable of experimental implementation, to measure replica symmetry breaking parameters in aging systems. The connection with the effective temperatures obtained from the fluctuation-dissipation theorem is discussed.\n
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\n \n\n \n \n \n \n \n \n Connectivities of Potts Fortuin–Kasteleyn clusters and time-like Liouville correlator.\n \n \n \n \n\n\n \n Picco, M.; Santachiara, R.; Viti, J.; and Delfino, G.\n\n\n \n\n\n\n Nuclear Physics B, 875(3): 719–737. oct 2013.\n \n\n\n\n
\n\n\n\n \n \n \"ConnectivitiesPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Picco2013,\nabstract = {Recently, two of us argued that the probability that an FK cluster in the Q-state Potts model connects three given points is related to the time-like Liouville three-point correlation function (Delfino and Viti, 2011) [1]. Moreover, they predicted that the FK three-point connectivity has a prefactor which unveils the effects of a discrete symmetry, reminiscent of the SQ permutation symmetry of the Q=2,3,4 Potts model. We revisit the derivation of the time-like Liouville correlator (Zamolodchikov, 2005) [2] and show that this is the only consistent analytic continuation of the minimal model structure constants. We then present strong numerical tests of the relation between the time-like Liouville correlator and percolative properties of the FK clusters for real values of Q.},\nauthor = {Picco, M. and Santachiara, R. and Viti, J. and Delfino, G.},\ndoi = {10.1016/j.nuclphysb.2013.07.014},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Picco et al. - 2013 - Connectivities of Potts Fortuin–Kasteleyn clusters and time-like Liouville correlator.pdf:pdf},\nissn = {05503213},\njournal = {Nuclear Physics B},\nmonth = {oct},\nnumber = {3},\npages = {719--737},\ntitle = {{Connectivities of Potts Fortuin–Kasteleyn clusters and time-like Liouville correlator}},\nurl = {http://www.sciencedirect.com/science/article/pii/S0550321313003805},\nvolume = {875},\nyear = {2013}\n}\n
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\n Recently, two of us argued that the probability that an FK cluster in the Q-state Potts model connects three given points is related to the time-like Liouville three-point correlation function (Delfino and Viti, 2011) [1]. Moreover, they predicted that the FK three-point connectivity has a prefactor which unveils the effects of a discrete symmetry, reminiscent of the SQ permutation symmetry of the Q=2,3,4 Potts model. We revisit the derivation of the time-like Liouville correlator (Zamolodchikov, 2005) [2] and show that this is the only consistent analytic continuation of the minimal model structure constants. We then present strong numerical tests of the relation between the time-like Liouville correlator and percolative properties of the FK clusters for real values of Q.\n
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\n \n\n \n \n \n \n \n \n Frozen into stripes: fate of the critical Ising model after a quench.\n \n \n \n \n\n\n \n Blanchard, T.; and Picco, M.\n\n\n \n\n\n\n Physical Review E, 88(3): 4. apr 2013.\n \n\n\n\n
\n\n\n\n \n \n \"FrozenPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n  \n \n 1 download\n \n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Blanchard2013c,\nabstract = {In this work we study numerically the final state of the two dimensional ferromagnetic critical Ising model after a quench to zero temperature. Beginning from equilibrium at {\\$}T{\\_}c{\\$}, the system can be blocked in a variety of infinitely long lived stripe states in addition to the ground state. Similar results have already been obtained for an infinite temperature initial condition and an interesting connection to exact percolation crossing probabilities has emerged. Here we complete this picture by providing a new example of stripe states precisely related to initial crossing probabilities for various boundary conditions. We thus show that this is not specific to percolation but rather that it depends on the properties of spanning clusters in the initial state.},\narchivePrefix = {arXiv},\narxivId = {1304.6758},\nauthor = {Blanchard, Thibault and Picco, Marco},\ndoi = {10.1103/PhysRevE.88.032131},\neprint = {1304.6758},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Blanchard, Picco - 2013 - Frozen into stripes Fate of the critical Ising model after a quench(5).pdf:pdf},\njournal = {Physical Review E},\nmonth = {apr},\nnumber = {3},\npages = {4},\npublisher = {American Physical Society},\nshorttitle = {Phys. Rev. E},\ntitle = {{Frozen into stripes: fate of the critical Ising model after a quench}},\nurl = {http://arxiv.org/abs/1304.6758 http://link.aps.org/doi/10.1103/PhysRevE.88.032131},\nvolume = {88},\nyear = {2013}\n}\n
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\n In this work we study numerically the final state of the two dimensional ferromagnetic critical Ising model after a quench to zero temperature. Beginning from equilibrium at $}T{_}c{$, the system can be blocked in a variety of infinitely long lived stripe states in addition to the ground state. Similar results have already been obtained for an infinite temperature initial condition and an interesting connection to exact percolation crossing probabilities has emerged. Here we complete this picture by providing a new example of stripe states precisely related to initial crossing probabilities for various boundary conditions. We thus show that this is not specific to percolation but rather that it depends on the properties of spanning clusters in the initial state.\n
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\n  \n 2012\n \n \n (2)\n \n \n
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\n \n\n \n \n \n \n \n \n A morphological study of cluster dynamics between critical points.\n \n \n \n \n\n\n \n Blanchard, T.; Cugliandolo, L. F.; and Picco, M.\n\n\n \n\n\n\n Journal of Statistical Mechanics: Theory and Experiment, 2012(05): P05026. may 2012.\n \n\n\n\n
\n\n\n\n \n \n \"APaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n\n\n\n
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@article{Blanchard2012,\nabstract = {We study the geometric properties of a system initially in equilibrium at a critical point that is suddenly quenched to another critical point and subsequently evolves towards the new equilibrium state. We focus on the bidimensional Ising model and we use numerical methods to characterize the morphological and statistical properties of spin and Fortuin-Kasteleyn clusters during the critical evolution. The analysis of the dynamics of an out of equilibrium interface is also performed. We show that the small scale properties, smaller than the target critical growing length xi(t) $\\backslash$simeq t{\\^{}}{\\{}1/z{\\}} with z the dynamic exponent, are characterized by equilibrium at the working critical point, while the large scale properties, larger than the critical growing length, are those of the initial critical point. These features are similar to what was found for sub-critical quenches. We argue that quenches between critical points could be amenable to a more detailed analytical description.},\narchivePrefix = {arXiv},\narxivId = {1203.6100},\nauthor = {Blanchard, Thibault and Cugliandolo, Leticia F. and Picco, Marco},\ndoi = {10.1088/1742-5468/2012/05/P05026},\neprint = {1203.6100},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Blanchard, Cugliandolo, Picco - 2012 - A morphological study of cluster dynamics between critical points.pdf:pdf},\nissn = {1742-5468},\njournal = {Journal of Statistical Mechanics: Theory and Experiment},\nkeywords = {Statistical Mechanics},\nmonth = {may},\nnumber = {05},\npages = {P05026},\ntitle = {{A morphological study of cluster dynamics between critical points}},\nurl = {http://arxiv.org/abs/1203.6100 http://stacks.iop.org/1742-5468/2012/i=05/a=P05026?key=crossref.8c5f0a30e65656923beb4542616c43ab},\nvolume = {2012},\nyear = {2012}\n}\n
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\n We study the geometric properties of a system initially in equilibrium at a critical point that is suddenly quenched to another critical point and subsequently evolves towards the new equilibrium state. We focus on the bidimensional Ising model and we use numerical methods to characterize the morphological and statistical properties of spin and Fortuin-Kasteleyn clusters during the critical evolution. The analysis of the dynamics of an out of equilibrium interface is also performed. We show that the small scale properties, smaller than the target critical growing length xi(t) $\\$simeq t^\\1/z\\ with z the dynamic exponent, are characterized by equilibrium at the working critical point, while the large scale properties, larger than the critical growing length, are those of the initial critical point. These features are similar to what was found for sub-critical quenches. We argue that quenches between critical points could be amenable to a more detailed analytical description.\n
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\n \n\n \n \n \n \n \n \n Critical behavior of the Ising model with long range interactions.\n \n \n \n \n\n\n \n Picco, M.\n\n\n \n\n\n\n ,5. jul 2012.\n \n\n\n\n
\n\n\n\n \n \n \"CriticalPaper\n  \n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n  \n \n 1 download\n \n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Picco2012,\nabstract = {We present results of a Monte Carlo study for the ferromagnetic Ising model with long range interactions in two dimensions. This model has been simulated for a large range of interaction parameter {\\$}\\backslashsigma{\\$} and for large sizes. We observe that the results close to the change of regime from intermediate to short range do not agree with the renormalization group predictions.},\narchivePrefix = {arXiv},\narxivId = {1207.1018},\nauthor = {Picco, Marco},\neprint = {1207.1018},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Picco - 2012 - Critical behavior of the Ising model with long range interactions.pdf:pdf},\nmonth = {jul},\npages = {5},\ntitle = {{Critical behavior of the Ising model with long range interactions}},\nurl = {http://arxiv.org/abs/1207.1018},\nyear = {2012}\n}\n
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\n We present results of a Monte Carlo study for the ferromagnetic Ising model with long range interactions in two dimensions. This model has been simulated for a large range of interaction parameter $}\\sigma{$ and for large sizes. We observe that the results close to the change of regime from intermediate to short range do not agree with the renormalization group predictions.\n
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\n  \n 2011\n \n \n (1)\n \n \n
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\n \n\n \n \n \n \n \n \n Critical interfaces and duality in the Ashkin-Teller model.\n \n \n \n \n\n\n \n Picco, M.; and Santachiara, R.\n\n\n \n\n\n\n Physical Review E, 83(6): 061124. nov 2011.\n \n\n\n\n
\n\n\n\n \n \n \"CriticalPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Picco2011,\nabstract = {We report on the numerical measures on different spin interfaces and FK cluster boundaries in the Askhin-Teller (AT) model. For a general point on the AT critical line, we find that the fractal dimension of a generic spin cluster interface can take one of four different possible values. In particular we found spin interfaces whose fractal dimension is d{\\_}f=3/2 all along the critical line. Further, the fractal dimension of the boundaries of FK clusters were found to satisfy all along the AT critical line a duality relation with the fractal dimension of their outer boundaries. This result provides a clear numerical evidence that such duality, which is well known in the case of the O(n) model, exists in a extended CFT.},\narchivePrefix = {arXiv},\narxivId = {1011.1159},\nauthor = {Picco, Marco and Santachiara, Raoul},\ndoi = {10.1103/PhysRevE.83.061124},\neprint = {1011.1159},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Picco, Santachiara - 2011 - Critical interfaces and duality in the Ashkin-Teller model.pdf:pdf},\nissn = {1539-3755},\njournal = {Physical Review E},\nmonth = {nov},\nnumber = {6},\npages = {061124},\npublisher = {American Physical Society},\nshorttitle = {Phys. Rev. E},\ntitle = {{Critical interfaces and duality in the Ashkin-Teller model}},\nurl = {http://arxiv.org/abs/1011.1159 http://pre.aps.org/abstract/PRE/v83/i6/e061124 http://link.aps.org/doi/10.1103/PhysRevE.83.061124},\nvolume = {83},\nyear = {2011}\n}\n
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\n We report on the numerical measures on different spin interfaces and FK cluster boundaries in the Askhin-Teller (AT) model. For a general point on the AT critical line, we find that the fractal dimension of a generic spin cluster interface can take one of four different possible values. In particular we found spin interfaces whose fractal dimension is d_f=3/2 all along the critical line. Further, the fractal dimension of the boundaries of FK clusters were found to satisfy all along the AT critical line a duality relation with the fractal dimension of their outer boundaries. This result provides a clear numerical evidence that such duality, which is well known in the case of the O(n) model, exists in a extended CFT.\n
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\n  \n 2010\n \n \n (1)\n \n \n
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\n \n\n \n \n \n \n \n \n Critical interfaces of the Ashkin-Teller model at the parafermionic point.\n \n \n \n \n\n\n \n Picco, M.; and Santachiara, R.\n\n\n \n\n\n\n Journal of Statistical Mechanics: Theory and Experiment, 2010(07): P07027. may 2010.\n \n\n\n\n
\n\n\n\n \n \n \"CriticalPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Picco2010,\nabstract = {We present an extensive study of interfaces defined in the Z{\\_}4 spin lattice representation of the Ashkin-Teller (AT) model. In particular, we numerically compute the fractal dimensions of boundary and bulk interfaces at the Fateev-Zamolodchikov point. This point is a special point on the self-dual critical line of the AT model and it is described in the continuum limit by the Z{\\_}4 parafermionic theory. Extending on previous analytical and numerical studies [10,12], we point out the existence of three different values of fractal dimensions which characterize different kind of interfaces. We argue that this result may be related to the classification of primary operators of the parafermionic algebra. The scenario emerging from the studies presented here is expected to unveil general aspects of geometrical objects of critical AT model, and thus of c=1 critical theories in general.},\narchivePrefix = {arXiv},\narxivId = {1005.0493},\nauthor = {Picco, Marco and Santachiara, Raoul},\ndoi = {10.1088/1742-5468/2010/07/P07027},\neprint = {1005.0493},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Picco, Santachiara - 2010 - Critical interfaces of the Ashkin-Teller model at the parafermionic point.pdf:pdf},\nissn = {1742-5468},\njournal = {Journal of Statistical Mechanics: Theory and Experiment},\nmonth = {may},\nnumber = {07},\npages = {P07027},\ntitle = {{Critical interfaces of the Ashkin-Teller model at the parafermionic point}},\nurl = {http://arxiv.org/abs/1005.0493 http://dx.doi.org/10.1088/1742-5468/2010/07/P07027},\nvolume = {2010},\nyear = {2010}\n}\n
\n
\n\n\n
\n We present an extensive study of interfaces defined in the Z_4 spin lattice representation of the Ashkin-Teller (AT) model. In particular, we numerically compute the fractal dimensions of boundary and bulk interfaces at the Fateev-Zamolodchikov point. This point is a special point on the self-dual critical line of the AT model and it is described in the continuum limit by the Z_4 parafermionic theory. Extending on previous analytical and numerical studies [10,12], we point out the existence of three different values of fractal dimensions which characterize different kind of interfaces. We argue that this result may be related to the classification of primary operators of the parafermionic algebra. The scenario emerging from the studies presented here is expected to unveil general aspects of geometrical objects of critical AT model, and thus of c=1 critical theories in general.\n
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\n  \n 2009\n \n \n (4)\n \n \n
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\n \n\n \n \n \n \n \n \n Stark effect of interactive electron–hole pairs in spherical semiconductor quantum dots.\n \n \n \n \n\n\n \n Billaud, B.; Picco, M.; and Truong, T.\n\n\n \n\n\n\n Journal of Physics: Condensed Matter, 21(39): 395302. sep 2009.\n \n\n\n\n
\n\n\n\n \n \n \"StarkPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Billaud2009,\nabstract = {We present a theoretical approach, based on the effective mass approximation model, on the quantum-confinement Stark effects for spherical semiconducting quantum dots in the regime of strong confinement of interactive electron-hole pairs and limiting weak electric field. The respective roles of Coulomb potential and polarization energy are investigated in detail. Under reasonable physical assumptions, analytical calculations can be performed. They show that the Stark shift is a quadratic function of the electric field amplitude in this regime. The computed numerical values obtained from this approach are found to be in good agreement with experimental data over a significant domain of quantum dot sizes.},\narchivePrefix = {arXiv},\narxivId = {0905.3080},\nauthor = {Billaud, B. and Picco, M. and Truong, T-T},\ndoi = {10.1088/0953-8984/21/39/395302},\neprint = {0905.3080},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Billaud, Picco, Truong - 2009 - Stark effect of interactive electron-hole pairs in spherical semiconductor quantum dots.pdf:pdf},\nissn = {0953-8984},\njournal = {Journal of Physics: Condensed Matter},\nmonth = {sep},\nnumber = {39},\npages = {395302},\npmid = {21832385},\ntitle = {{Stark effect of interactive electron–hole pairs in spherical semiconductor quantum dots}},\nurl = {http://arxiv.org/abs/0905.3080 http://stacks.iop.org/0953-8984/21/i=39/a=395302?key=crossref.52e9fac48a4b0e13e67ee32207313468},\nvolume = {21},\nyear = {2009}\n}\n
\n
\n\n\n
\n We present a theoretical approach, based on the effective mass approximation model, on the quantum-confinement Stark effects for spherical semiconducting quantum dots in the regime of strong confinement of interactive electron-hole pairs and limiting weak electric field. The respective roles of Coulomb potential and polarization energy are investigated in detail. Under reasonable physical assumptions, analytical calculations can be performed. They show that the Stark shift is a quadratic function of the electric field amplitude in this regime. The computed numerical values obtained from this approach are found to be in good agreement with experimental data over a significant domain of quantum dot sizes.\n
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\n \n\n \n \n \n \n \n \n New Theoretical Approach to Quantum Size Effects of Interactive Electron-hole in Spherical Semiconductor Quantum Dots.\n \n \n \n \n\n\n \n Billaud, B.; Picco, M.; and Truong, T. T.\n\n\n \n\n\n\n . mar 2009.\n \n\n\n\n
\n\n\n\n \n \n \"NewPaper\n  \n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
\n
@article{Billaud2009a,\nabstract = {The issue of quantum size effects of interactive electron-hole systems in spherical semiconductor quantum dots is put to question. A sharper theoretical approach is suggested based on a new pseudo-potential method. In this new setting, analytical computations can be performed in most intermediate steps lending stronger support to the adopted physical assumptions. The resulting numerical values for physical quantities are found to be much closer to the experimental values than those existing so far in the literature.},\narchivePrefix = {arXiv},\narxivId = {0903.4021},\nauthor = {Billaud, Baptiste and Picco, Marco and Truong, T. T.},\neprint = {0903.4021},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Billaud, Picco, Truong - 2009 - New Theoretical Approach to Quantum Size Effects of Interactive Electron-hole in Spherical Semiconductor.pdf:pdf},\nmonth = {mar},\ntitle = {{New Theoretical Approach to Quantum Size Effects of Interactive Electron-hole in Spherical Semiconductor Quantum Dots}},\nurl = {http://arxiv.org/abs/0903.4021},\nyear = {2009}\n}\n
\n
\n\n\n
\n The issue of quantum size effects of interactive electron-hole systems in spherical semiconductor quantum dots is put to question. A sharper theoretical approach is suggested based on a new pseudo-potential method. In this new setting, analytical computations can be performed in most intermediate steps lending stronger support to the adopted physical assumptions. The resulting numerical values for physical quantities are found to be much closer to the experimental values than those existing so far in the literature.\n
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\n \n\n \n \n \n \n \n \n Critical Interfaces in the Random-Bond Potts Model.\n \n \n \n \n\n\n \n Jacobsen, J.; Le Doussal, P.; Picco, M.; Santachiara, R.; and Wiese, K.\n\n\n \n\n\n\n Physical Review Letters, 102(7): 4. feb 2009.\n \n\n\n\n
\n\n\n\n \n \n \"CriticalPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n\n\n\n
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@article{Jacobsen2009,\nabstract = {We study geometrical properties of interfaces in the random-temperature q-states Potts model as an example of a conformal field theory weakly perturbed by quenched disorder. Using conformal perturbation theory in q-2 we compute the fractal dimension of Fortuin Kasteleyn domain walls. We also compute it numerically both via the Wolff cluster algorithm for q=3 and via transfer-matrix evaluations. We obtain numerical results for the fractal dimension of spin cluster interfaces for q=3. These are found numerically consistent with the duality kappa(spin) * kappa(FK)= 16 as expressed in putative SLE parameters.},\narchivePrefix = {arXiv},\narxivId = {0809.3985},\nauthor = {Jacobsen, Jesper and {Le Doussal}, Pierre and Picco, Marco and Santachiara, Raoul and Wiese, Kay},\ndoi = {10.1103/PhysRevLett.102.070601},\neprint = {0809.3985},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Jacobsen et al. - 2009 - Critical Interfaces in the Random-Bond Potts Model(2).pdf:pdf},\nissn = {0031-9007},\njournal = {Physical Review Letters},\nkeywords = {Disordered Systems and Neural Networks},\nmonth = {feb},\nnumber = {7},\npages = {4},\ntitle = {{Critical Interfaces in the Random-Bond Potts Model}},\nurl = {http://arxiv.org/abs/0809.3985 http://link.aps.org/doi/10.1103/PhysRevLett.102.070601},\nvolume = {102},\nyear = {2009}\n}\n
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\n\n\n
\n We study geometrical properties of interfaces in the random-temperature q-states Potts model as an example of a conformal field theory weakly perturbed by quenched disorder. Using conformal perturbation theory in q-2 we compute the fractal dimension of Fortuin Kasteleyn domain walls. We also compute it numerically both via the Wolff cluster algorithm for q=3 and via transfer-matrix evaluations. We obtain numerical results for the fractal dimension of spin cluster interfaces for q=3. These are found numerically consistent with the duality kappa(spin) * kappa(FK)= 16 as expressed in putative SLE parameters.\n
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\n \n\n \n \n \n \n \n \n Geometrical properties of parafermionic spin models.\n \n \n \n \n\n\n \n Picco, M.; Santachiara, R.; and Sicilia, A.\n\n\n \n\n\n\n Journal of Statistical Mechanics: Theory and Experiment, 2009(04): P04013. apr 2009.\n \n\n\n\n
\n\n\n\n \n \n \"GeometricalPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Picco2009,\nabstract = {We present measurements of the fractal dimensions associated to the geometrical clusters for Z{\\_}4 and Z{\\_}5 spin models. We also attempted to measure similar fractal dimensions for the generalised Fortuyin Kastelyn (FK) clusters in these models but we discovered that these clusters do not percolate at the critical point of the model under consideration. These results clearly mark a difference in the behaviour of these non local objects compared to the Ising model or the 3-state Potts model which corresponds to the simplest cases of Z{\\_}N spin models with N=2 and N=3 respectively. We compare these fractal dimensions with the ones obtained for SLE interfaces.},\narchivePrefix = {arXiv},\narxivId = {0812.3526},\nauthor = {Picco, Marco and Santachiara, Raoul and Sicilia, Alberto},\ndoi = {10.1088/1742-5468/2009/04/P04013},\neprint = {0812.3526},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Picco, Santachiara, Sicilia - 2009 - Geometrical properties of parafermionic spin models.pdf:pdf},\nissn = {1742-5468},\njournal = {Journal of Statistical Mechanics: Theory and Experiment},\nmonth = {apr},\nnumber = {04},\npages = {P04013},\ntitle = {{Geometrical properties of parafermionic spin models}},\nurl = {http://arxiv.org/abs/0812.3526 http://stacks.iop.org/1742-5468/2009/i=04/a=P04013?key=crossref.576dd5b206dfc9813952efce744b70c2},\nvolume = {2009},\nyear = {2009}\n}\n
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\n We present measurements of the fractal dimensions associated to the geometrical clusters for Z_4 and Z_5 spin models. We also attempted to measure similar fractal dimensions for the generalised Fortuyin Kastelyn (FK) clusters in these models but we discovered that these clusters do not percolate at the critical point of the model under consideration. These results clearly mark a difference in the behaviour of these non local objects compared to the Ising model or the 3-state Potts model which corresponds to the simplest cases of Z_N spin models with N=2 and N=3 respectively. We compare these fractal dimensions with the ones obtained for SLE interfaces.\n
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\n  \n 2008\n \n \n (1)\n \n \n
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\n \n\n \n \n \n \n \n \n Scaling and super-universality in the coarsening dynamics of the 3D random field Ising model.\n \n \n \n \n\n\n \n Aron, C.; Chamon, C.; Cugliandolo, L. F.; and Picco, M.\n\n\n \n\n\n\n Journal of Statistical Mechanics: Theory and Experiment, 2008(05): P05016. may 2008.\n \n\n\n\n
\n\n\n\n \n \n \"ScalingPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n \n \n\n\n\n
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@article{Aron2008,\nabstract = {We study the coarsening dynamics of the three-dimensional random field Ising model using Monte Carlo numerical simulations. We test the dynamic scaling and super-scaling properties of global and local two-time observables. We treat in parallel the three-dimensional Edward-Anderson spin-glass and we recall results on Lennard-Jones mixtures and colloidal suspensions to highlight the common and different out of equilibrium properties of these glassy systems.},\narchivePrefix = {arXiv},\narxivId = {0803.0664},\nauthor = {Aron, Camille and Chamon, Claudio and Cugliandolo, Leticia F. and Picco, Marco},\ndoi = {10.1088/1742-5468/2008/05/P05016},\neprint = {0803.0664},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Aron et al. - 2008 - Scaling and super-universality in the coarsening dynamics of the 3D random field Ising model.pdf:pdf},\nissn = {1742-5468},\njournal = {Journal of Statistical Mechanics: Theory and Experiment},\nkeywords = {Disordered Systems and Neural Networks,Statistical Mechanics},\nmonth = {may},\nnumber = {05},\npages = {P05016},\ntitle = {{Scaling and super-universality in the coarsening dynamics of the 3D random field Ising model}},\nurl = {http://arxiv.org/abs/0803.0664 http://stacks.iop.org/1742-5468/2008/i=05/a=P05016?key=crossref.373de04d6b1a47306d8b58e45d15b389},\nvolume = {2008},\nyear = {2008}\n}\n
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\n We study the coarsening dynamics of the three-dimensional random field Ising model using Monte Carlo numerical simulations. We test the dynamic scaling and super-scaling properties of global and local two-time observables. We treat in parallel the three-dimensional Edward-Anderson spin-glass and we recall results on Lennard-Jones mixtures and colloidal suspensions to highlight the common and different out of equilibrium properties of these glassy systems.\n
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\n  \n 2007\n \n \n (2)\n \n \n
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\n \n\n \n \n \n \n \n \n Growing dynamical length, scaling, and heterogeneities in the 3D Edwards–Anderson model.\n \n \n \n \n\n\n \n Jaubert, L. D. C.; Chamon, C.; Cugliandolo, L. F.; and Picco, M.\n\n\n \n\n\n\n Journal of Statistical Mechanics: Theory and Experiment, 2007(05): 24. may 2007.\n \n\n\n\n
\n\n\n\n \n \n \"GrowingPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n\n\n\n
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@article{Jaubert2007,\nabstract = {We study numerically spatio-temporal fluctuations during the out-of-equilibrium relaxation of the three-dimensional Edwards-Anderson model. We focus on two issues. (1) The evolution of a growing dynamical length scale in the glassy phase of the model, and the consequent collapse of the distribution of local coarse-grained correlations measured at different pairs of times on a single function using {\\{}$\\backslash$it two{\\}} scaling parameters, the value of the global correlation at the measuring times and the ratio of the coarse graining length to the dynamical length scale (in the thermodynamic limit). (2) The `triangular' relation between coarse-grained local correlations at three pairs of times taken from the ordered instants {\\$}t{\\_}3 \\backslashleq t{\\_}2 \\backslashleq t{\\_}1{\\$}. Property (1) is consistent with the conjecture that the development of time-reparametrization invariance asymptotically is responsible for the main dynamic fluctuations in aging glassy systems as well as with other mechanisms proposed in the literature. Property (2), we stress, is a much stronger test of the relevance of the time-reparametrization invariance scenario.},\nannote = {From Duplicate 1 ( \n\nGrowing dynamical length, scaling, and heterogeneities in the 3D Edwards–Anderson model\n\n- Jaubert, Ludovic D. C.; Chamon, Claudio; Cugliandolo, Leticia F.; Picco, Marco )\n\n},\narchivePrefix = {arXiv},\narxivId = {cond-mat/0701116},\nauthor = {Jaubert, Ludovic D. C. and Chamon, Claudio and Cugliandolo, Leticia F. and Picco, Marco},\ndoi = {10.1088/1742-5468/2007/05/P05001},\neprint = {0701116},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Jaubert et al. - 2007 - Growing dynamical length, scaling, and heterogeneities in the 3D Edwards–Anderson model.pdf:pdf},\nissn = {1742-5468},\njournal = {Journal of Statistical Mechanics: Theory and Experiment},\nkeywords = {Disordered Systems and Neural Networks},\nmonth = {may},\nnumber = {05},\npages = {24},\nprimaryClass = {cond-mat},\npublisher = {IOP PUBLISHING LTD},\ntitle = {{Growing dynamical length, scaling, and heterogeneities in the 3D Edwards–Anderson model}},\nurl = {http://arxiv.org/abs/cond-mat/0701116 http://stacks.iop.org/1742-5468/2007/i=05/a=P05001?key=crossref.a6fdbeaf3197b47fa265b83aa9ea42f8},\nvolume = {2007},\nyear = {2007}\n}\n
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\n We study numerically spatio-temporal fluctuations during the out-of-equilibrium relaxation of the three-dimensional Edwards-Anderson model. We focus on two issues. (1) The evolution of a growing dynamical length scale in the glassy phase of the model, and the consequent collapse of the distribution of local coarse-grained correlations measured at different pairs of times on a single function using \\$\\$it two\\ scaling parameters, the value of the global correlation at the measuring times and the ratio of the coarse graining length to the dynamical length scale (in the thermodynamic limit). (2) The `triangular' relation between coarse-grained local correlations at three pairs of times taken from the ordered instants $}t{_}3 \\leq t{_}2 \\leq t{_}1{$. Property (1) is consistent with the conjecture that the development of time-reparametrization invariance asymptotically is responsible for the main dynamic fluctuations in aging glassy systems as well as with other mechanisms proposed in the literature. Property (2), we stress, is a much stronger test of the relevance of the time-reparametrization invariance scenario.\n
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\n \n\n \n \n \n \n \n \n Numerical study on schramm-loewner evolution in nonminimal conformal field theories.\n \n \n \n \n\n\n \n Picco, M.; and Santachiara, R.\n\n\n \n\n\n\n Physical Review Letters, 100(1): 4. jan 2007.\n \n\n\n\n
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@article{Picco2007,\nabstract = {The Schramm-Loewner evolution (SLE) is a powerful tool to describe fractal interfaces in 2D critical statistical systems. Yet the application of SLE is well established for statistical systems described by quantum field theories satisfying only conformal invariance, the so called minimal conformal field theories (CFTs). We consider interfaces in Z(N) spin models at their self-dual critical point for N=4 and N=5. These lattice models are described in the continuum limit by non-minimal CFTs where the role of a ZN symmetry, in addition to the conformal one, should be taken into account. We provide numerical results on the fractal dimension of the interfaces which are SLE candidates for non-minimal CFTs. Our results are in excellent agreement with some recent theoretical predictions.},\narchivePrefix = {arXiv},\narxivId = {0708.4295},\nauthor = {Picco, Marco and Santachiara, Raoul},\ndoi = {10.1103/PhysRevLett.100.015704},\neprint = {0708.4295},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Picco, Santachiara - 2007 - Numerical study on schramm-loewner evolution in nonminimal conformal field theories(3).pdf:pdf},\ninstitution = {LPTHE, Universit{\\'{e}} Pierre et Marie Curie-Paris6, 4 Place Jussieu, 75005 Paris, France. picco@lpthe.jussieu.fr},\nissn = {0031-9007},\njournal = {Physical Review Letters},\nmonth = {jan},\nnumber = {1},\npages = {4},\ntitle = {{Numerical study on schramm-loewner evolution in nonminimal conformal field theories.}},\nurl = {http://arxiv.org/abs/0708.4295 http://link.aps.org/doi/10.1103/PhysRevLett.100.015704},\nvolume = {100},\nyear = {2007}\n}\n
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\n The Schramm-Loewner evolution (SLE) is a powerful tool to describe fractal interfaces in 2D critical statistical systems. Yet the application of SLE is well established for statistical systems described by quantum field theories satisfying only conformal invariance, the so called minimal conformal field theories (CFTs). We consider interfaces in Z(N) spin models at their self-dual critical point for N=4 and N=5. These lattice models are described in the continuum limit by non-minimal CFTs where the role of a ZN symmetry, in addition to the conformal one, should be taken into account. We provide numerical results on the fractal dimension of the interfaces which are SLE candidates for non-minimal CFTs. Our results are in excellent agreement with some recent theoretical predictions.\n
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\n  \n 2006\n \n \n (1)\n \n \n
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\n \n\n \n \n \n \n \n \n Strong disorder fixed points in the two-dimensional random-bond Ising model.\n \n \n \n \n\n\n \n Picco, M.; Honecker, A.; and Pujol, P.\n\n\n \n\n\n\n Journal of Statistical Mechanics: Theory and Experiment, 2006(09): P09006–P09006. sep 2006.\n \n\n\n\n
\n\n\n\n \n \n \"StrongPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n  \n \n 1 download\n \n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n \n \n \n \n \n \n\n\n\n
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@article{Picco2006,\nabstract = {The random-bond Ising model on the square lattice has several disordered critical points, depending on the probability distribution of the bonds. There are a finite-temperature multicritical point, called Nishimori point, and a zero-temperature fixed point, for both a binary distribution where the coupling constants take the values +/- J and a Gaussian disorder distribution. Inclusion of dilution in the +/- J distribution (J=0 for some bonds) gives rise to another zero-temperature fixed point which can be identified with percolation in the non-frustrated case (J {\\textgreater}= 0). We study these fixed points using numerical (transfer matrix) methods. We determine the location, critical exponents, and central charge of the different fixed points and study the spin-spin correlation functions. Our main findings are the following: (1) We confirm that the Nishimori point is universal with respect to the type of disorder, i.e. we obtain the same central charge and critical exponents for the +/- J and Gaussian distributions of disorder. (2) The Nishimori point, the zero-temperature fixed point for the +/- J and Gaussian distributions of disorder, and the percolation point in the diluted case all belong to mutually distinct universality classes. (3) The paramagnetic phase is re-entrant below the Nishimori point, i.e. the zero-temperature fixed points are not located exactly below the Nishimori point, neither for the +/- J distribution, nor for the Gaussian distribution.},\narchivePrefix = {arXiv},\narxivId = {cond-mat/0606312},\nauthor = {Picco, Marco and Honecker, Andreas and Pujol, Pierre},\ndoi = {10.1088/1742-5468/2006/09/P09006},\neprint = {0606312},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Picco, Honecker, Pujol - 2006 - Strong disorder fixed points in the two-dimensional random-bond Ising model(2).pdf:pdf},\nissn = {1742-5468},\njournal = {Journal of Statistical Mechanics: Theory and Experiment},\nkeywords = {Classical phase transitions (theory),Conformal field theory (theory),Disordered systems (theory),Renormalization group},\nmonth = {sep},\nnumber = {09},\npages = {P09006--P09006},\nprimaryClass = {cond-mat},\ntitle = {{Strong disorder fixed points in the two-dimensional random-bond Ising model}},\nurl = {http://arxiv.org/abs/cond-mat/0606312 http://stacks.iop.org/1742-5468/2006/i=09/a=P09006?key=crossref.42340f86308ee12f1b2817bbb64ceb04},\nvolume = {2006},\nyear = {2006}\n}\n
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\n The random-bond Ising model on the square lattice has several disordered critical points, depending on the probability distribution of the bonds. There are a finite-temperature multicritical point, called Nishimori point, and a zero-temperature fixed point, for both a binary distribution where the coupling constants take the values +/- J and a Gaussian disorder distribution. Inclusion of dilution in the +/- J distribution (J=0 for some bonds) gives rise to another zero-temperature fixed point which can be identified with percolation in the non-frustrated case (J \\textgreater= 0). We study these fixed points using numerical (transfer matrix) methods. We determine the location, critical exponents, and central charge of the different fixed points and study the spin-spin correlation functions. Our main findings are the following: (1) We confirm that the Nishimori point is universal with respect to the type of disorder, i.e. we obtain the same central charge and critical exponents for the +/- J and Gaussian distributions of disorder. (2) The Nishimori point, the zero-temperature fixed point for the +/- J and Gaussian distributions of disorder, and the percolation point in the diluted case all belong to mutually distinct universality classes. (3) The paramagnetic phase is re-entrant below the Nishimori point, i.e. the zero-temperature fixed points are not located exactly below the Nishimori point, neither for the +/- J distribution, nor for the Gaussian distribution.\n
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\n  \n 2004\n \n \n (3)\n \n \n
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\n \n\n \n \n \n \n \n \n Dynamical AC study of the critical behavior in Heisenberg spin glasses.\n \n \n \n \n\n\n \n Picco, M.; and Ritort, F.\n\n\n \n\n\n\n Physical Review B, 71(10): 7. 2004.\n \n\n\n\n
\n\n\n\n \n \n \"DynamicalPaper\n  \n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Picco2004a,\nabstract = {We present some numerical results for the Heisenberg spin-glass model with Gaussian interactions, in a three dimensional cubic lattice. We measure the AC susceptibility as a function of temperature and determine an apparent finite temperature transition which is compatible with the chiral-glass temperature transition for this model. The relaxation time diverges like a power law tausim (T-Tc) -znu with Tc=0.19(4) and znu=5.0(5). Although our data indicates that the spin-glass transition occurs at the same temperature as the chiral glass transition, we cannot exclude the possibility of a chiral-spin coupling scenario for the lowest frequencies investigated.},\nauthor = {Picco, Marco and Ritort, Felix},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Picco, Ritort - 2004 - Dynamical AC study of the critical behavior in Heisenberg spin glasses.pdf:pdf},\njournal = {Physical Review B},\nnumber = {10},\npages = {7},\ntitle = {{Dynamical AC study of the critical behavior in Heisenberg spin glasses}},\nurl = {http://arxiv.org/abs/cond-mat/0405308},\nvolume = {71},\nyear = {2004}\n}\n
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\n We present some numerical results for the Heisenberg spin-glass model with Gaussian interactions, in a three dimensional cubic lattice. We measure the AC susceptibility as a function of temperature and determine an apparent finite temperature transition which is compatible with the chiral-glass temperature transition for this model. The relaxation time diverges like a power law tausim (T-Tc) -znu with Tc=0.19(4) and znu=5.0(5). Although our data indicates that the spin-glass transition occurs at the same temperature as the chiral glass transition, we cannot exclude the possibility of a chiral-spin coupling scenario for the lowest frequencies investigated.\n
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\n \n\n \n \n \n \n \n \n Self-duality for coupled Potts models on the triangular lattice.\n \n \n \n \n\n\n \n Richard, J. J.; Jacobsen, J. J. L.; and Picco, M.\n\n\n \n\n\n\n Journal of Physics A: Mathematical and General, 37(18): 4939–4954. may 2004.\n \n\n\n\n
\n\n\n\n \n \n \"Self-dualityPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n\n\n\n
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@article{Richard2004,\nabstract = {We present selfdual manifolds for coupled Potts models on the triangular lattice. We exploit two different techniques: duality followed by decimation, and mapping to a related loop model. The latter technique is found to be superior, and it allows to include three-spin couplings. Starting from three coupled models, such couplings are necessary for generating selfdual solutions. A numerical study of the case of two coupled models leads to the identification of novel critical points.},\narchivePrefix = {arXiv},\narxivId = {cond-mat/0402420},\nauthor = {Richard, J.-F. Jean-Fran{\\c{c}}ois and Jacobsen, J.L. Jesper Lykke and Picco, Marco},\ndoi = {10.1088/0305-4470/37/18/003},\neprint = {0402420},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Richard, Jacobsen, Picco - 2004 - Self-duality for coupled Potts models on the triangular lattice.pdf:pdf},\nissn = {0305-4470},\njournal = {Journal of Physics A: Mathematical and General},\nkeywords = {Statistical Mechanics},\nmonth = {may},\nnumber = {18},\npages = {4939--4954},\nprimaryClass = {cond-mat},\ntitle = {{Self-duality for coupled Potts models on the triangular lattice}},\nurl = {http://arxiv.org/abs/cond-mat/0402420 http://stacks.iop.org/0305-4470/37/i=18/a=003?key=crossref.01b1f94f632351dd8acfc00060b77045},\nvolume = {37},\nyear = {2004}\n}\n
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\n We present selfdual manifolds for coupled Potts models on the triangular lattice. We exploit two different techniques: duality followed by decimation, and mapping to a related loop model. The latter technique is found to be superior, and it allows to include three-spin couplings. Starting from three coupled models, such couplings are necessary for generating selfdual solutions. A numerical study of the case of two coupled models leads to the identification of novel critical points.\n
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\n \n\n \n \n \n \n \n \n Scale invariance and self-averaging in disordered systems.\n \n \n \n \n\n\n \n Parisi, G.; Picco, M.; and Sourlas, N.\n\n\n \n\n\n\n Europhysics Letters (EPL), 66(4): 465–470. may 2004.\n \n\n\n\n
\n\n\n\n \n \n \"ScalePaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n \n \n\n\n\n
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@article{Parisi2004,\nabstract = {In a previous paper we found that in the random field Ising model at zero temperature in three dimensions the correlation length is not self-averaging near the critical point and that the violation of self-averaging is maximal. This is due to the formation of bound states in the underlying field theory. We present a similar study for the case of disordered Potts and Ising ferromagnets in two dimensions near the critical temperature. In the random Potts model the correlation length is not self-averaging near the critical temperature but the violation of self-averaging is weaker than in the random field case. In the random Ising model we find still weaker violations of self-averaging and we cannot rule out the possibility of the restoration of self-averaging in the infinite volume limit.},\nannote = {From Duplicate 2 (Scale invariance and self-averaging in disordered systems - Parisi, Giorgio; Picco, Marco; Sourlas, Nicolas)\n\nFrom Duplicate 2 ( \n\nScale invariance and self-averaging in disordered systems\n\n- Parisi, Giorgio; Picco, Marco; Sourlas, Nicolas )\n\n},\narchivePrefix = {arXiv},\narxivId = {cond-mat/0312715},\nauthor = {Parisi, Giorgio and Picco, Marco and Sourlas, Nicolas},\ndoi = {10.1209/epl/i2004-10014-0},\neprint = {0312715},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Parisi, Picco, Sourlas - 2004 - Scale invariance and self-averaging in disordered systems.pdf:pdf},\nissn = {0295-5075},\njournal = {Europhysics Letters (EPL)},\nkeywords = {Disordered Systems and Neural Networks,Statistical Mechanics},\nmonth = {may},\nnumber = {4},\npages = {465--470},\nprimaryClass = {cond-mat},\ntitle = {{Scale invariance and self-averaging in disordered systems}},\nurl = {http://arxiv.org/abs/cond-mat/0312715 http://stacks.iop.org/0295-5075/66/i=4/a=465?key=crossref.3b96a888f56dac830a3f9022fd5fa6e8},\nvolume = {66},\nyear = {2004}\n}\n
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\n In a previous paper we found that in the random field Ising model at zero temperature in three dimensions the correlation length is not self-averaging near the critical point and that the violation of self-averaging is maximal. This is due to the formation of bound states in the underlying field theory. We present a similar study for the case of disordered Potts and Ising ferromagnets in two dimensions near the critical temperature. In the random Potts model the correlation length is not self-averaging near the critical temperature but the violation of self-averaging is weaker than in the random field case. In the random Ising model we find still weaker violations of self-averaging and we cannot rule out the possibility of the restoration of self-averaging in the infinite volume limit.\n
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\n  \n 2003\n \n \n (1)\n \n \n
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\n \n\n \n \n \n \n \n \n Statistics of lowest droplets in two-dimensional Gaussian Ising spin glasses.\n \n \n \n \n\n\n \n Picco, M.; Ritort, F.; and Sales, M.\n\n\n \n\n\n\n Physical Review B, 67(18): 22. may 2003.\n \n\n\n\n
\n\n\n\n \n \n \"StatisticsPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n\n\n\n
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@article{Picco2003,\nabstract = {A new approach to determine the value of the zero-temperature thermal exponent theta in spin glasses is presented. It consists in describing the energy level spectrum in spin glasses only in terms of the properties of the lowest energy droplets and the lowest droplet exponents (LDEs) lambda{\\_}l,theta{\\_}l that describe the statistics of their sizes and gaps. We show how these LDEs yield the standard thermal exponent of droplet theory theta through the relation, theta=theta{\\_}l+d*lambda{\\_}l. The present approach provides a new way to measure the thermal exponent theta without any assumption about the correct procedure to generate typical low-lying excitations as is commonly done in many perturbation methods including domain wall calculations. To illustrate the usefulness of the method we present a detailed investigation of the properties of the lowest energy droplets in two-dimensional Gaussian Ising spin glasses. By independent measurements of both LDEs and an aspect-ratio analysis, we find theta(2d) {\\~{}}- 0.46(1){\\textless} theta{\\_}{\\{}DW{\\}}(2d) {\\~{}}- 0.287 where theta{\\_}{\\{}DW{\\}} is the thermal exponent obtained in domain-wall theory. We also discuss the origin of finite-volume corrections in the behavior of the LDE theta{\\_}l and relate them to the finite-volume corrections in the statistics of extreme values. All in all, we show that typical large-scale droplets are not probed by most of the present perturbation methods as they probably do not have a compact structure as has been recently suggested.},\narchivePrefix = {arXiv},\narxivId = {cond-mat/0210576},\nauthor = {Picco, M. and Ritort, F. and Sales, M.},\ndoi = {10.1103/PhysRevB.67.184421},\neprint = {0210576},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Picco, Ritort, Sales - Unknown - Statistics of lowest droplets in two-dimensional Gaussian Ising spin glasses.pdf:pdf},\nissn = {0163-1829},\njournal = {Physical Review B},\nkeywords = {condensed matter},\nmonth = {may},\nnumber = {18},\npages = {22},\nprimaryClass = {cond-mat},\ntitle = {{Statistics of lowest droplets in two-dimensional Gaussian Ising spin glasses}},\nurl = {http://arxiv.org/abs/cond-mat/0210576 http://link.aps.org/doi/10.1103/PhysRevB.67.184421},\nvolume = {67},\nyear = {2003}\n}\n
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\n A new approach to determine the value of the zero-temperature thermal exponent theta in spin glasses is presented. It consists in describing the energy level spectrum in spin glasses only in terms of the properties of the lowest energy droplets and the lowest droplet exponents (LDEs) lambda_l,theta_l that describe the statistics of their sizes and gaps. We show how these LDEs yield the standard thermal exponent of droplet theory theta through the relation, theta=theta_l+d*lambda_l. The present approach provides a new way to measure the thermal exponent theta without any assumption about the correct procedure to generate typical low-lying excitations as is commonly done in many perturbation methods including domain wall calculations. To illustrate the usefulness of the method we present a detailed investigation of the properties of the lowest energy droplets in two-dimensional Gaussian Ising spin glasses. By independent measurements of both LDEs and an aspect-ratio analysis, we find theta(2d) \\ - 0.46(1)\\textless theta_\\DW\\(2d) \\ - 0.287 where theta_\\DW\\ is the thermal exponent obtained in domain-wall theory. We also discuss the origin of finite-volume corrections in the behavior of the LDE theta_l and relate them to the finite-volume corrections in the statistics of extreme values. All in all, we show that typical large-scale droplets are not probed by most of the present perturbation methods as they probably do not have a compact structure as has been recently suggested.\n
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\n  \n 2002\n \n \n (2)\n \n \n
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\n \n\n \n \n \n \n \n \n Phase diagram and critical exponents of a Potts gauge glass.\n \n \n \n \n\n\n \n Jacobsen, J. L.; and Picco, M.\n\n\n \n\n\n\n Physical Review E, 65(2): 026113. jan 2002.\n \n\n\n\n
\n\n\n\n \n \n \"PhasePaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Jacobsen2002b,\nabstract = {The two-dimensional q-state Potts model is subjected to a Z{\\_}q symmetric disorder that allows for the existence of a Nishimori line. At q=2, this model coincides with the +/- J random-bond Ising model. For q{\\textgreater}2, apart from the usual pure and zero-temperature fixed points, the ferro/paramagnetic phase boundary is controlled by two critical fixed points: a weak disorder point, whose universality class is that of the ferromagnetic bond-disordered Potts model, and a strong disorder point which generalizes the usual Nishimori point. We numerically study the case q=3, tracing out the phase diagram and precisely determining the critical exponents. The universality class of the Nishimori point is inconsistent with percolation on Potts clusters.},\narchivePrefix = {arXiv},\narxivId = {cond-mat/0105587},\nauthor = {Jacobsen, Jesper Lykke and Picco, Marco},\ndoi = {10.1103/PhysRevE.65.026113},\neprint = {0105587},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Jacobsen, Picco - 2002 - Phase diagram and critical exponents of a Potts gauge glass.pdf:pdf},\nissn = {1063-651X},\njournal = {Physical Review E},\nmonth = {jan},\nnumber = {2},\npages = {026113},\nprimaryClass = {cond-mat},\ntitle = {{Phase diagram and critical exponents of a Potts gauge glass}},\nurl = {http://arxiv.org/abs/cond-mat/0105587 http://link.aps.org/doi/10.1103/PhysRevE.65.026113},\nvolume = {65},\nyear = {2002}\n}\n
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\n The two-dimensional q-state Potts model is subjected to a Z_q symmetric disorder that allows for the existence of a Nishimori line. At q=2, this model coincides with the +/- J random-bond Ising model. For q\\textgreater2, apart from the usual pure and zero-temperature fixed points, the ferro/paramagnetic phase boundary is controlled by two critical fixed points: a weak disorder point, whose universality class is that of the ferromagnetic bond-disordered Potts model, and a strong disorder point which generalizes the usual Nishimori point. We numerically study the case q=3, tracing out the phase diagram and precisely determining the critical exponents. The universality class of the Nishimori point is inconsistent with percolation on Potts clusters.\n
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\n \n\n \n \n \n \n \n \n Nishimori Point in Random-Bond Ising and Potts Models in 2D.\n \n \n \n \n\n\n \n Honecker, A.; Jacobsen, J. L.; Picco, M.; and Pujol, P.\n\n\n \n\n\n\n In Statistical Field Theories, pages 251–261. Springer Netherlands, Dordrecht, 2002.\n \n\n\n\n
\n\n\n\n \n \n \"NishimoriPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n\n \n  \n \n 1 download\n \n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@incollection{Honecker2002,\naddress = {Dordrecht},\nauthor = {Honecker, Andreas and Jacobsen, Jesper L. and Picco, Marco and Pujol, Pierre},\nbooktitle = {Statistical Field Theories},\ndoi = {10.1007/978-94-010-0514-2_23},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Honecker et al. - 2002 - Nishimori Point in Random-Bond Ising and Potts Models in 2D.pdf:pdf},\npages = {251--261},\npublisher = {Springer Netherlands},\ntitle = {{Nishimori Point in Random-Bond Ising and Potts Models in 2D}},\nurl = {http://link.springer.com/10.1007/978-94-010-0514-2{\\_}23},\nyear = {2002}\n}\n
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\n  \n 2001\n \n \n (6)\n \n \n
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\n \n\n \n \n \n \n \n \n Aging effects and dynamic scaling in the 3d Edwards-Anderson spin glasses: a comparison with experiments.\n \n \n \n \n\n\n \n Picco, M.; Ricci-Tersenghi, F.; and Ritort, F.\n\n\n \n\n\n\n The European Physical Journal B Condensed Matter and Complex Systems, 21(2): 6. 2001.\n \n\n\n\n
\n\n\n\n \n \n \"AgingPaper\n  \n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n \n \n \n \n\n\n\n
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@article{Picco2001d,\nabstract = {We present a detailed study of the scaling behavior of correlations functions and AC susceptibility relaxations in the aging regime in three dimensional spin glasses. The agreement between simulations and experiments is excellent confirming the validity of the full aging scenario with logarithmic corrections which manifests as weak sub-aging effects.},\nauthor = {Picco, M. and Ricci-Tersenghi, F. and Ritort, F.},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Picco, Ricci-Tersenghi, Ritort - 2001 - Aging effects and dynamic scaling in the 3d Edwards-Anderson spin glasses a comparison with expe.pdf:pdf},\nissn = {14346028},\njournal = {The European Physical Journal B Condensed Matter and Complex Systems},\nkeywords = {75.10.Nr Spin-glass and other random models,75.40.Gb Dynamic properties (dynamic susceptibilit,75.40.Mg Numerical simulation studies},\nnumber = {2},\npages = {6},\ntitle = {{Aging effects and dynamic scaling in the 3d Edwards-Anderson spin glasses: a comparison with experiments}},\nurl = {http://arxiv.org/abs/cond-mat/0102248},\nvolume = {21},\nyear = {2001}\n}\n
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\n We present a detailed study of the scaling behavior of correlations functions and AC susceptibility relaxations in the aging regime in three dimensional spin glasses. The agreement between simulations and experiments is excellent confirming the validity of the full aging scenario with logarithmic corrections which manifests as weak sub-aging effects.\n
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\n \n\n \n \n \n \n \n \n Chaotic, memory, and cooling rate effects in spin glasses: Evaluation of the Edwards-Anderson model.\n \n \n \n \n\n\n \n Picco, M.; Ricci-Tersenghi, F.; and Ritort, F.\n\n\n \n\n\n\n Physical Review B, 63(17): 174412. apr 2001.\n \n\n\n\n
\n\n\n\n \n \n \"Chaotic,Paper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Picco2001c,\nabstract = {We investigate chaotic, memory and cooling rate effects in the three dimensional Edwards-Anderson model by doing thermoremanent (TRM) and AC susceptibility numerical experiments and making a detailed comparison with laboratory experiments on spin glasses. In contrast to the experiments, the Edwards-Anderson model does not show any trace of re-initialization processes in temperature change experiments (TRM or AC). A detailed comparison with AC relaxation experiments in the presence of DC magnetic field or coupling distribution perturbations reveals that the absence of chaotic effects in the Edwards-Anderson model is a consequence of the presence of strong cooling rate effects. We discuss possible solutions to this discrepancy, in particular the smallness of the time scales reached in numerical experiments, but we also question the validity of the Edwards-Anderson model to reproduce the experimental results.},\narchivePrefix = {arXiv},\narxivId = {cond-mat/0005541},\nauthor = {Picco, Marco and Ricci-Tersenghi, Federico and Ritort, Felix},\ndoi = {10.1103/PhysRevB.63.174412},\neprint = {0005541},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Picco, Ricci-Tersenghi, Ritort - 2001 - Chaotic, memory, and cooling rate effects in spin glasses Evaluation of the Edwards-Anderson (2).pdf:pdf},\nissn = {0163-1829},\njournal = {Physical Review B},\nmonth = {apr},\nnumber = {17},\npages = {174412},\nprimaryClass = {cond-mat},\ntitle = {{Chaotic, memory, and cooling rate effects in spin glasses: Evaluation of the Edwards-Anderson model}},\nurl = {http://arxiv.org/abs/cond-mat/0005541},\nvolume = {63},\nyear = {2001}\n}\n
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\n We investigate chaotic, memory and cooling rate effects in the three dimensional Edwards-Anderson model by doing thermoremanent (TRM) and AC susceptibility numerical experiments and making a detailed comparison with laboratory experiments on spin glasses. In contrast to the experiments, the Edwards-Anderson model does not show any trace of re-initialization processes in temperature change experiments (TRM or AC). A detailed comparison with AC relaxation experiments in the presence of DC magnetic field or coupling distribution perturbations reveals that the absence of chaotic effects in the Edwards-Anderson model is a consequence of the presence of strong cooling rate effects. We discuss possible solutions to this discrepancy, in particular the smallness of the time scales reached in numerical experiments, but we also question the validity of the Edwards-Anderson model to reproduce the experimental results.\n
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\n \n\n \n \n \n \n \n \n Random energy levels and low-temperature expansions for spin glasses.\n \n \n \n \n\n\n \n Picco, M.; Ritort, F.; and Sales, M.\n\n\n \n\n\n\n ,6. jun 2001.\n \n\n\n\n
\n\n\n\n \n \n \"RandomPaper\n  \n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Picco2001,\nabstract = {In a previous paper (cond-mat/0106554) we showed the existence of two new zero-temperature exponents ($\\backslash$lambda and $\\backslash$theta') in two dimensional Gaussian spin glasses. Here we introduce a novel low-temperature expansion for spin glasses expressed in terms of the gap probability distributions for successive energy levels. After presenting the numerical evidence in favor of a random-energy levels scenario, we analyze the main consequences on the low-temperature equilibrium behavior. We find that the specific heat is anomalous at low-temperatures c {\\~{}} T**$\\backslash$alpha with $\\backslash$alpha=-d/$\\backslash$theta' which turns out to be linear for the case $\\backslash$theta'=-d.},\narchivePrefix = {arXiv},\narxivId = {cond-mat/0106592},\nauthor = {Picco, M. and Ritort, F. and Sales, M.},\neprint = {0106592},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Picco, Ritort, Sales - 2001 - Random energy levels and low-temperature expansions for spin glasses.pdf:pdf},\nmonth = {jun},\npages = {6},\nprimaryClass = {cond-mat},\ntitle = {{Random energy levels and low-temperature expansions for spin glasses}},\nurl = {http://arxiv.org/abs/cond-mat/0106592},\nyear = {2001}\n}\n
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\n In a previous paper (cond-mat/0106554) we showed the existence of two new zero-temperature exponents ($\\$lambda and $\\$theta') in two dimensional Gaussian spin glasses. Here we introduce a novel low-temperature expansion for spin glasses expressed in terms of the gap probability distributions for successive energy levels. After presenting the numerical evidence in favor of a random-energy levels scenario, we analyze the main consequences on the low-temperature equilibrium behavior. We find that the specific heat is anomalous at low-temperatures c \\  T**$\\$alpha with $\\$alpha=-d/$\\$theta' which turns out to be linear for the case $\\$theta'=-d.\n
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\n \n\n \n \n \n \n \n \n Universality Class of the Nishimori Point in the 2D ±J Random-Bond Ising Model.\n \n \n \n \n\n\n \n Honecker, A.; Picco, M.; and Pujol, P.\n\n\n \n\n\n\n Physical review letters, 87(4): 047201. jul 2001.\n \n\n\n\n
\n\n\n\n \n \n \"UniversalityPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n  \n \n 1 download\n \n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Honecker2001a,\nabstract = {We study the universality class of the Nishimori point in the 2D ±J random-bond Ising model by means of the numerical transfer-matrix method. Using the domain-wall free energy, we locate the position of the fixed point along the Nishimori line at the critical concentration value pc = 0.1094±0.0002 and estimate $\\nu$ = 1.33±0.03. Then, we obtain the exponents for the moments of the spin-spin correlation functions as well as the value for the central charge c = 0.464±0.004. The main qualitative result is the fact that percolation is now excluded as a candidate for describing the universality class of this fixed point.},\nauthor = {Honecker, A. and Picco, M. and Pujol, P.},\ndoi = {10.1103/PhysRevLett.87.047201},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Honecker, Picco, Pujol - 2001 - Universality Class of the Nishimori Point in the 2D ±J Random-Bond Ising Model.pdf:pdf},\ninstitution = {Institut f{\\"{u}}r Theoretische Physik, TU Braunschweig, Mendelssohnstrasse 3, 38106 Braunschweig, Germany.},\nissn = {0031-9007},\njournal = {Physical review letters},\nmonth = {jul},\nnumber = {4},\npages = {047201},\npmid = {11461639},\npublisher = {American Physical Society},\nshorttitle = {Phys. Rev. Lett.},\ntitle = {{Universality Class of the Nishimori Point in the 2D ±J Random-Bond Ising Model}},\nurl = {http://link.aps.org/doi/10.1103/PhysRevLett.87.047201 http://www.ncbi.nlm.nih.gov/pubmed/11461639},\nvolume = {87},\nyear = {2001}\n}\n
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\n We study the universality class of the Nishimori point in the 2D ±J random-bond Ising model by means of the numerical transfer-matrix method. Using the domain-wall free energy, we locate the position of the fixed point along the Nishimori line at the critical concentration value pc = 0.1094±0.0002 and estimate $ν$ = 1.33±0.03. Then, we obtain the exponents for the moments of the spin-spin correlation functions as well as the value for the central charge c = 0.464±0.004. The main qualitative result is the fact that percolation is now excluded as a candidate for describing the universality class of this fixed point.\n
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\n \n\n \n \n \n \n \n \n Order-parameter fluctuations (OPF) in spin glasses: Monte Carlo simulations and exact results for small sizes.\n \n \n \n \n\n\n \n Picco, M.; Ritort, F.; and Sales, M.\n\n\n \n\n\n\n The European Physical Journal B, 19(4): 565–582. feb 2001.\n \n\n\n\n
\n\n\n\n \n \n \"Order-parameterPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Picco2001a,\nabstract = {The use of parameters measuring order-parameter fluctuations (OPF) has been encouraged by the recent results reported in $\\backslash$cite{\\{}RS{\\}} which show that two of these parameters, {\\$}G{\\$} and {\\$}G{\\_}c{\\$}, take universal values in the {\\$}\\backslashlim{\\_}{\\{}T\\backslashto 0{\\}}{\\$}. In this paper we present a detailed study of parameters measuring OPF for two mean-field models with and without time-reversal symmetry which exhibit different patterns of replica symmetry breaking below the transition: the Sherrington-Kirkpatrick model with and without a field and the Ising p-spin glass (p=3). We give numerical results and analyze the consequences which replica equivalence imposes on these models in the infinite volume. We give evidence for the transition in each system and discuss the character of finite-size effects. Furthermore, a comparative study between this new family of parameters and the usual Binder cumulant analysis shows what kind of new information can be extracted from the finite {\\$}T{\\$} behavior of these quantities. The two main outcomes of this work are: 1) Parameters measuring OPF give better estimates than the Binder cumulant for {\\$}T{\\_}c{\\$} and even for very small systems they give evidence for the transition. 2) For systems with no time-reversal symmetry, parameters defined in terms of connected quantities are the proper ones to look at.},\narchivePrefix = {arXiv},\narxivId = {cond-mat/0009292},\nauthor = {Picco, Marco and Ritort, Felix and Sales, Marta},\ndoi = {10.1007/s100510170302},\neprint = {0009292},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Picco, Ritort, Sales - 2008 - Order-parameter fluctuations (OPF) in spin glasses Monte Carlo simulations and exact results for small sizes.pdf:pdf},\nissn = {1434-6028},\njournal = {The European Physical Journal B},\nmonth = {feb},\nnumber = {4},\npages = {565--582},\nprimaryClass = {cond-mat},\ntitle = {{Order-parameter fluctuations (OPF) in spin glasses: Monte Carlo simulations and exact results for small sizes}},\nurl = {http://arxiv.org/abs/cond-mat/0009292 http://www.springerlink.com/index/10.1007/s100510170302},\nvolume = {19},\nyear = {2001}\n}\n
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\n The use of parameters measuring order-parameter fluctuations (OPF) has been encouraged by the recent results reported in $\\$cite\\RS\\ which show that two of these parameters, $}G{$ and $}G{_}c{$, take universal values in the $}\\lim{_}{\\{}T\\to 0{\\}}{$. In this paper we present a detailed study of parameters measuring OPF for two mean-field models with and without time-reversal symmetry which exhibit different patterns of replica symmetry breaking below the transition: the Sherrington-Kirkpatrick model with and without a field and the Ising p-spin glass (p=3). We give numerical results and analyze the consequences which replica equivalence imposes on these models in the infinite volume. We give evidence for the transition in each system and discuss the character of finite-size effects. Furthermore, a comparative study between this new family of parameters and the usual Binder cumulant analysis shows what kind of new information can be extracted from the finite $}T{$ behavior of these quantities. The two main outcomes of this work are: 1) Parameters measuring OPF give better estimates than the Binder cumulant for $}T{_}c{$ and even for very small systems they give evidence for the transition. 2) For systems with no time-reversal symmetry, parameters defined in terms of connected quantities are the proper ones to look at.\n
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\n \n\n \n \n \n \n \n \n Classification of conformal field theories based on Coulomb gases. Application to loop models.\n \n \n \n \n\n\n \n Dotsenko, V. V. S.; Jacobsen, J. J. L.; and Picco, M.\n\n\n \n\n\n\n Nuclear Physics B, 618(3): 523–550. dec 2001.\n \n\n\n\n
\n\n\n\n \n \n \"ClassificationPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n \n \n \n \n\n\n\n
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@article{Dotsenko2001,\nabstract = {We present a method for classifying conformal field theories based on Coulomb gases (bosonic free-field construction). Given a particular geometric configuration of the screening charges, we give necessary conditions for the existence of degenerate representations and for the closure of the vertex-operator algebra. The resulting classification contains, but is more general than, the standard one based on classical Lie algebras. We then apply the method to the Coulomb gas theory for the two-flavoured loop model of Jacobsen and Kondev. The purpose of the study is to clarify the relation between Coulomb gas models and conformal field theories with extended symmetries.},\narchivePrefix = {arXiv},\narxivId = {hep-th/0105287},\nauthor = {Dotsenko, V.S. Vladimir S. and Jacobsen, J.L. Jesper Lykke and Picco, Marco},\ndoi = {10.1016/S0550-3213(01)00409-6},\neprint = {0105287},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Dotsenko, Jacobsen, Picco - 2001 - Classification of conformal field theories based on Coulomb gases. Application to loop models(2).pdf:pdf},\nissn = {05503213},\njournal = {Nuclear Physics B},\nkeywords = {05.50.+q,64.60.Fr,75.10.Hk},\nmonth = {dec},\nnumber = {3},\npages = {523--550},\nprimaryClass = {hep-th},\ntitle = {{Classification of conformal field theories based on Coulomb gases. Application to loop models}},\nurl = {http://arxiv.org/abs/hep-th/0105287},\nvolume = {618},\nyear = {2001}\n}\n
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\n\n\n
\n We present a method for classifying conformal field theories based on Coulomb gases (bosonic free-field construction). Given a particular geometric configuration of the screening charges, we give necessary conditions for the existence of degenerate representations and for the closure of the vertex-operator algebra. The resulting classification contains, but is more general than, the standard one based on classical Lie algebras. We then apply the method to the Coulomb gas theory for the two-flavoured loop model of Jacobsen and Kondev. The purpose of the study is to clarify the relation between Coulomb gas models and conformal field theories with extended symmetries.\n
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\n  \n 2000\n \n \n (2)\n \n \n
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\n \n\n \n \n \n \n \n \n Regular bouncing cosmological solutions in effective actions in four dimensions.\n \n \n \n \n\n\n \n Constantinidis, C. P.; Fabris, J. C.; Furtado, R. G.; and Picco, M.\n\n\n \n\n\n\n Physical Review D, 61(4): 043503. jan 2000.\n \n\n\n\n
\n\n\n\n \n \n \"RegularPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Constantinidis2000,\nabstract = {We study cosmological scenarios resulting from effective actions in four dimensions which are, under some assumptions, connected with multidimensional, supergravity and string theories. These effective actions are labeled by the parameters {\\$}\\backslashomega{\\$}, the dilaton coupling constant, and {\\$}n{\\$} which establishes the coupling between the dilaton and a scalar field originated from the gauge field existing in the original theories. There is a large class of bouncing as well as Friedmann-like solutions. We investigate under which conditions bouncing regular solutions can be obtained. In the case of the string effective action, regularity is obtained through the inclusion of contributions from the Ramond-Ramond sector of superstring.},\narchivePrefix = {arXiv},\narxivId = {gr-qc/9906122},\nauthor = {Constantinidis, C.P. P. and Fabris, J.C. C. and Furtado, R.G. G. and Picco, M.},\ndoi = {10.1103/PhysRevD.61.043503},\neprint = {9906122},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Constantinidis et al. - 2000 - Regular bouncing cosmological solutions in effective actions in four dimensions(2).pdf:pdf},\nissn = {0556-2821},\njournal = {Physical Review D},\nmonth = {jan},\nnumber = {4},\npages = {043503},\nprimaryClass = {gr-qc},\ntitle = {{Regular bouncing cosmological solutions in effective actions in four dimensions}},\nurl = {http://arxiv.org/abs/gr-qc/9906122 https://link.aps.org/doi/10.1103/PhysRevD.61.043503},\nvolume = {61},\nyear = {2000}\n}\n
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\n We study cosmological scenarios resulting from effective actions in four dimensions which are, under some assumptions, connected with multidimensional, supergravity and string theories. These effective actions are labeled by the parameters $}\\omega{$, the dilaton coupling constant, and $}n{$ which establishes the coupling between the dilaton and a scalar field originated from the gauge field existing in the original theories. There is a large class of bouncing as well as Friedmann-like solutions. We investigate under which conditions bouncing regular solutions can be obtained. In the case of the string effective action, regularity is obtained through the inclusion of contributions from the Ramond-Ramond sector of superstring.\n
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\n \n\n \n \n \n \n \n \n Large- q asymptotics of the random-bond Potts model.\n \n \n \n \n\n\n \n Jacobsen, J. L.; and Picco, M.\n\n\n \n\n\n\n Physical Review E, 61(1): R13–R16. jan 2000.\n \n\n\n\n
\n\n\n\n \n \n \"Large-Paper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Jacobsen2000a,\nabstract = {We numerically examine the large-q asymptotics of the q-state random bond Potts model. Special attention is paid to the parametrisation of the critical line, which is determined by combining the loop representation of the transfer matrix with Zamolodchikov's c-theorem. Asymptotically the central charge seems to behave like c(q) = 1/2 log{\\_}2(q) + O(1). Very accurate values of the bulk magnetic exponent x{\\_}1 are then extracted by performing Monte Carlo simulations directly at the critical point. As q -{\\textgreater} infinity, these seem to tend to a non-trivial limit, x{\\_}1 -{\\textgreater} 0.192 +- 0.002.},\narchivePrefix = {arXiv},\narxivId = {cond-mat/9910071},\nauthor = {Jacobsen, Jesper Lykke and Picco, Marco},\ndoi = {10.1103/PhysRevE.61.R13},\neprint = {9910071},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Jacobsen, Picco - 2000 - Large- q asymptotics of the random-bond Potts model.pdf:pdf},\nissn = {1063-651X},\njournal = {Physical Review E},\nmonth = {jan},\nnumber = {1},\npages = {R13--R16},\nprimaryClass = {cond-mat},\ntitle = {{Large- q asymptotics of the random-bond Potts model}},\nurl = {http://arxiv.org/abs/cond-mat/9910071 http://link.aps.org/doi/10.1103/PhysRevE.61.R13 https://link.aps.org/doi/10.1103/PhysRevE.61.R13},\nvolume = {61},\nyear = {2000}\n}\n
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\n We numerically examine the large-q asymptotics of the q-state random bond Potts model. Special attention is paid to the parametrisation of the critical line, which is determined by combining the loop representation of the transfer matrix with Zamolodchikov's c-theorem. Asymptotically the central charge seems to behave like c(q) = 1/2 log_2(q) + O(1). Very accurate values of the bulk magnetic exponent x_1 are then extracted by performing Monte Carlo simulations directly at the critical point. As q -\\textgreater infinity, these seem to tend to a non-trivial limit, x_1 -\\textgreater 0.192 +- 0.002.\n
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\n  \n 1999\n \n \n (3)\n \n \n
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\n \n\n \n \n \n \n \n \n Continuous phase transition in a spin-glass model without time-reversal symmetry.\n \n \n \n \n\n\n \n Parisi, G.; Picco, M.; and Ritort, F.\n\n\n \n\n\n\n Physical Review E, 60(1): 58–68. jul 1999.\n \n\n\n\n
\n\n\n\n \n \n \"ContinuousPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Parisi1999,\nabstract = {We investigate the phase transition in a strongly disordered short-range three-spin interaction model characterized by the absence of time reversal symmetry in the Hamiltonian. In the mean-field limit the model is well described by the Adam-Gibbs-DiMarzio scenario for the glass transition; however in the short-range case this picture turns out to be modified. The model presents a finite temperature continuous phase transition characterized by a divergent spin-glass susceptibility and a negative specific heat exponent. We expect the nature of the transition in this 3-spin model to be the same as the transition in the Edwards-Anderson model in a magnetic field, with the advantage that the strong crossover effects present in the latter case are absent.},\nauthor = {Parisi, G. and Picco, M. and Ritort, F.},\ndoi = {10.1103/PhysRevE.60.58},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Parisi, Picco, Ritort - 1999 - Continuous phase transition in a spin-glass model without time-reversal symmetry.pdf:pdf},\ninstitution = {Dipartimento di Fisica and INFN, Universita di Roma La Sapienza, Piazzale Aldo Moro 2, 00185 Roma, Italy. giorgio.paresi@roma1.infn.it},\nissn = {1063-651X},\njournal = {Physical Review E},\nmonth = {jul},\nnumber = {1},\npages = {58--68},\ntitle = {{Continuous phase transition in a spin-glass model without time-reversal symmetry}},\nurl = {http://arxiv.org/abs/cond-mat/9812230 https://link.aps.org/doi/10.1103/PhysRevE.60.58},\nvolume = {60},\nyear = {1999}\n}\n
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\n We investigate the phase transition in a strongly disordered short-range three-spin interaction model characterized by the absence of time reversal symmetry in the Hamiltonian. In the mean-field limit the model is well described by the Adam-Gibbs-DiMarzio scenario for the glass transition; however in the short-range case this picture turns out to be modified. The model presents a finite temperature continuous phase transition characterized by a divergent spin-glass susceptibility and a negative specific heat exponent. We expect the nature of the transition in this 3-spin model to be the same as the transition in the Edwards-Anderson model in a magnetic field, with the advantage that the strong crossover effects present in the latter case are absent.\n
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\n \n\n \n \n \n \n \n \n Marinari et al. Reply:.\n \n \n \n \n\n\n \n Marinari, E.; Naitza, C.; Zuliani, F.; Parisi, G.; Picco, M.; and Ritort, F.\n\n\n \n\n\n\n Physical Review Letters, 82(25): 5175–5175. jun 1999.\n \n\n\n\n
\n\n\n\n \n \n \"MarinariPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Marinari1999,\nabstract = {A Reply to the Comment by Hemant Bokil et al.},\nauthor = {Marinari, E. and Naitza, C. and Zuliani, F. and Parisi, G. and Picco, M. and Ritort, F.},\ndoi = {10.1103/PhysRevLett.82.5175},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Marinari et al. - 1999 - Marinari et al. Reply.pdf:pdf},\nissn = {0031-9007},\njournal = {Physical Review Letters},\nmonth = {jun},\nnumber = {25},\npages = {5175--5175},\npublisher = {American Physical Society},\nshorttitle = {Phys. Rev. Lett.},\ntitle = {{Marinari et al. Reply:}},\nurl = {http://link.aps.org/doi/10.1103/PhysRevLett.82.5175},\nvolume = {82},\nyear = {1999}\n}\n
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\n A Reply to the Comment by Hemant Bokil et al.\n
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\n \n\n \n \n \n \n \n \n Coupled Potts models: Self-duality and fixed point structure.\n \n \n \n \n\n\n \n Dotsenko, V.; Jacobsen, J. J. L.; Lewis, M. M.; and Picco, M.\n\n\n \n\n\n\n Nuclear Physics B, 546(3): 505–557. may 1999.\n \n\n\n\n
\n\n\n\n \n \n \"CoupledPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n \n \n \n \n \n \n \n \n\n\n\n
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@article{Dotsenko1999,\nabstract = {We consider q-state Potts models coupled by their energy operators. Restricting our study to self-dual couplings, numerical simulations demonstrate the existence of non-trivial fixed points for 2 {\\textless}= q {\\textless}= 4. These fixed points were first predicted by perturbative renormalisation group calculations. Accurate values for the central charge and the multiscaling exponents of the spin and energy operators are calculated using a series of novel transfer matrix algorithms employing clusters and loops. These results compare well with those of the perturbative expansion, in the range of parameter values where the latter is valid. The criticality of the fixed-point models is independently verified by examining higher eigenvalues in the even sector, and by demonstrating the existence of scaling laws from Monte Carlo simulations. This might be a first step towards the identification of the conformal field theories describing the critical behaviour of this class of models.},\narchivePrefix = {arXiv},\narxivId = {cond-mat/9812227},\nauthor = {Dotsenko, Vladimir and Jacobsen, J.L. Jesper Lykke and Lewis, M.-A. Marc-Andr{\\'{e}} and Picco, Marco},\ndoi = {10.1016/S0550-3213(99)00097-8},\neprint = {9812227},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Dotsenko et al. - 1999 - Coupled Potts models Self-duality and fixed point structure.pdf:pdf},\nissn = {05503213},\njournal = {Nuclear Physics B},\nkeywords = {Duality transformation,Multiscaling,Perturbative renormalisation group,Potts model,Transfer matrix},\nmonth = {may},\nnumber = {3},\npages = {505--557},\nprimaryClass = {cond-mat},\ntitle = {{Coupled Potts models: Self-duality and fixed point structure}},\nurl = {http://arxiv.org/abs/cond-mat/9812227 http://linkinghub.elsevier.com/retrieve/pii/S0550321399000978},\nvolume = {546},\nyear = {1999}\n}\n
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\n We consider q-state Potts models coupled by their energy operators. Restricting our study to self-dual couplings, numerical simulations demonstrate the existence of non-trivial fixed points for 2 \\textless= q \\textless= 4. These fixed points were first predicted by perturbative renormalisation group calculations. Accurate values for the central charge and the multiscaling exponents of the spin and energy operators are calculated using a series of novel transfer matrix algorithms employing clusters and loops. These results compare well with those of the perturbative expansion, in the range of parameter values where the latter is valid. The criticality of the fixed-point models is independently verified by examining higher eigenvalues in the even sector, and by demonstrating the existence of scaling laws from Monte Carlo simulations. This might be a first step towards the identification of the conformal field theories describing the critical behaviour of this class of models.\n
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\n  \n 1998\n \n \n (4)\n \n \n
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\n \n\n \n \n \n \n \n \n Random bond Potts model: The test of the replica symmetry breaking.\n \n \n \n \n\n\n \n Dotsenko, V.; Dotsenko, V.; and Picco, M.\n\n\n \n\n\n\n Nuclear Physics B, 520(3): 633–674. jun 1998.\n \n\n\n\n
\n\n\n\n \n \n \"RandomPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Dotsenko1998,\nabstract = {Averaged spin-spin correlation function squared {\\$}\\backslashoverline{\\{}{\\textless}\\backslashsigma(0)\\backslashsigma(R){\\textgreater}{\\^{}}{\\{}2{\\}}{\\}}{\\$} is calculated for the ferromagnetic random bond Potts model. The technique being used is the renormalization group plus conformal field theory. The results are of the {\\$}\\backslashepsilon{\\$} - expansion type fixed point calculation, {\\$}\\backslashepsilon{\\$} being the deviation of the central charge (or the number of components) of the Potts model from the Ising model value. Calculations are done both for the replica symmetric and the replica symmetry broken fixed points. The results obtained allow for the numerical simulation tests to decide between the two different criticalities of the random bond Potts model.},\narchivePrefix = {arXiv},\narxivId = {hep-th/9709136},\nauthor = {Dotsenko, V.S. and Dotsenko, Vl.S. and Picco, M.},\ndoi = {10.1016/S0550-3213(98)00183-7},\neprint = {9709136},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Dotsenko, Dotsenko, Picco - 1998 - Random bond Potts model The test of the replica symmetry breaking(2).pdf:pdf},\nissn = {05503213},\njournal = {Nuclear Physics B},\nmonth = {jun},\nnumber = {3},\npages = {633--674},\nprimaryClass = {hep-th},\ntitle = {{Random bond Potts model: The test of the replica symmetry breaking}},\nurl = {http://arxiv.org/abs/hep-th/9709136 https://linkinghub.elsevier.com/retrieve/pii/S0550321398001837},\nvolume = {520},\nyear = {1998}\n}\n
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\n Averaged spin-spin correlation function squared $}\\overline{\\{}{\\textless}\\sigma(0)\\sigma(R){\\textgreater}{^}{\\{}2{\\}}{\\}}{$ is calculated for the ferromagnetic random bond Potts model. The technique being used is the renormalization group plus conformal field theory. The results are of the $}\\epsilon{$ - expansion type fixed point calculation, $}\\epsilon{$ being the deviation of the central charge (or the number of components) of the Potts model from the Ising model value. Calculations are done both for the replica symmetric and the replica symmetry broken fixed points. The results obtained allow for the numerical simulation tests to decide between the two different criticalities of the random bond Potts model.\n
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\n \n\n \n \n \n \n \n \n Tempering simulations in the four dimensional ±J Ising spin glass in a magnetic field.\n \n \n \n \n\n\n \n Picco, M.; and Ritort, F.\n\n\n \n\n\n\n Physica A: Statistical Mechanics and its Applications, 250(1-4): 46–57. feb 1998.\n \n\n\n\n
\n\n\n\n \n \n \"TemperingPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Picco1998,\nabstract = {We study the four dimensional (4D) {\\$}\\backslashpm J{\\$} Ising spin glass in a magnetic field by using the simulated tempering method recently introduced by Marinari and Parisi. We compute numerically the first four moments of the order parameter probability distribution {\\$}P(q){\\$}. We find a finite cusp in the spin-glass susceptibility and strong tendency to paramagnetic ordering at low temperatures. Assuming a well defined transition we are able to bound its critical temperature.},\narchivePrefix = {arXiv},\narxivId = {cond-mat/9702041},\nauthor = {Picco, Marco and Ritort, Felix},\ndoi = {10.1016/S0378-4371(97)00545-1},\neprint = {9702041},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Picco, Ritort - 1997 - Tempering simulations in the four dimensional -J Ising spin glass in a magnetic field.pdf:pdf},\nissn = {03784371},\njournal = {Physica A: Statistical Mechanics and its Applications},\nmonth = {feb},\nnumber = {1-4},\npages = {46--57},\nprimaryClass = {cond-mat},\ntitle = {{Tempering simulations in the four dimensional ±J Ising spin glass in a magnetic field}},\nurl = {http://arxiv.org/abs/cond-mat/9702041 http://dx.doi.org/10.1016/S0378-4371(97)00545-1 http://linkinghub.elsevier.com/retrieve/pii/S0378437197005451},\nvolume = {250},\nyear = {1998}\n}\n
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\n\n\n
\n We study the four dimensional (4D) $}\\pm J{$ Ising spin glass in a magnetic field by using the simulated tempering method recently introduced by Marinari and Parisi. We compute numerically the first four moments of the order parameter probability distribution $}P(q){$. We find a finite cusp in the spin-glass susceptibility and strong tendency to paramagnetic ordering at low temperatures. Assuming a well defined transition we are able to bound its critical temperature.\n
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\n \n\n \n \n \n \n \n \n A Study of Cross-Over Effects For The 2D Random Bond Potts Model.\n \n \n \n \n\n\n \n Picco, M.\n\n\n \n\n\n\n ,12. feb 1998.\n \n\n\n\n
\n\n\n\n \n \n \"APaper\n  \n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
\n
@article{Picco1998a,\nabstract = {We present results of a numerical simulation of the {\\$}q{\\$}-state random bond Potts model in two dimensions and for large {\\$}q{\\$}. In particular, care is taken to study the crossover from the pure model to the random model, as well as the crossover from the percolation to the random model. We show how to determine precisely the random fixed point and measure critical exponents at this point.},\narchivePrefix = {arXiv},\narxivId = {cond-mat/9802092},\nauthor = {Picco, Marco},\neprint = {9802092},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Picco - 1998 - A Study of Cross-Over Effects For The 2D Random Bond Potts Model.pdf:pdf},\nmonth = {feb},\npages = {12},\nprimaryClass = {cond-mat},\ntitle = {{A Study of Cross-Over Effects For The 2D Random Bond Potts Model}},\nurl = {http://arxiv.org/abs/cond-mat/9802092},\nyear = {1998}\n}\n
\n
\n\n\n
\n We present results of a numerical simulation of the $}q{$-state random bond Potts model in two dimensions and for large $}q{$. In particular, care is taken to study the crossover from the pure model to the random model, as well as the crossover from the percolation to the random model. We show how to determine precisely the random fixed point and measure critical exponents at this point.\n
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\n \n\n \n \n \n \n \n \n General Method to Determine Replica Symmetry Breaking Transitions.\n \n \n \n \n\n\n \n Marinari, E.; Naitza, C.; Zuliani, F.; Parisi, G.; Picco, M.; and Ritort, F.\n\n\n \n\n\n\n Physical Review Letters, 81(8): 1698–1701. aug 1998.\n \n\n\n\n
\n\n\n\n \n \n \"GeneralPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
\n
@article{Marinari1998,\nabstract = {We introduce a new parameter to investigate replica symmetry breaking transitions using finite-size scaling methods. Based on exact equalities initially derived by F. Guerra this parameter is a direct check of the self-averaging character of the spin-glass order parameter. This new parameter can be used to study models with time reversal symmetry but its greatest interest lies in models where this symmetry is absent. We apply the method to long-range and short-range Ising spin-glasses with and without a magnetic field as well as short-range multispin interaction spin-glasses.},\nauthor = {Marinari, E. and Naitza, C. and Zuliani, F. and Parisi, G. and Picco, M. and Ritort, F.},\ndoi = {10.1103/PhysRevLett.81.1698},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Marinari et al. - 1998 - General Method to Determine Replica Symmetry Breaking Transitions.pdf:pdf},\nissn = {0031-9007},\njournal = {Physical Review Letters},\nmonth = {aug},\nnumber = {8},\npages = {1698--1701},\npublisher = {American Physical Society},\nshorttitle = {Phys. Rev. Lett.},\ntitle = {{General Method to Determine Replica Symmetry Breaking Transitions}},\nurl = {http://link.aps.org/doi/10.1103/PhysRevLett.81.1698},\nvolume = {81},\nyear = {1998}\n}\n
\n
\n\n\n
\n We introduce a new parameter to investigate replica symmetry breaking transitions using finite-size scaling methods. Based on exact equalities initially derived by F. Guerra this parameter is a direct check of the self-averaging character of the spin-glass order parameter. This new parameter can be used to study models with time reversal symmetry but its greatest interest lies in models where this symmetry is absent. We apply the method to long-range and short-range Ising spin-glasses with and without a magnetic field as well as short-range multispin interaction spin-glasses.\n
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\n  \n 1997\n \n \n (2)\n \n \n
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\n \n\n \n \n \n \n \n \n Weak Randomness for Large q-State Potts Models in Two Dimensions.\n \n \n \n \n\n\n \n Picco, M.\n\n\n \n\n\n\n Physical Review Letters, 79(16): 2998–3001. oct 1997.\n \n\n\n\n
\n\n\n\n \n \n \"WeakPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
\n
@article{Picco1997,\nabstract = {We have studied the effect of weak randomness on q-state Potts models for q{\\textgreater}4 by measuring the central charges of these models using transfer matrix methods. We obtain a set of new values for the central charges and then show that some of these values are related to one another by a factorization law.},\nauthor = {Picco, M.},\ndoi = {10.1103/PhysRevLett.79.2998},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Picco - 1997 - Weak Randomness for Large q-State Potts Models in Two Dimensions(2).pdf:pdf},\nissn = {0031-9007},\njournal = {Physical Review Letters},\nmonth = {oct},\nnumber = {16},\npages = {2998--3001},\npublisher = {American Physical Society},\nshorttitle = {Phys. Rev. Lett.},\ntitle = {{Weak Randomness for Large q-State Potts Models in Two Dimensions}},\nurl = {http://link.aps.org/doi/10.1103/PhysRevLett.79.2998},\nvolume = {79},\nyear = {1997}\n}\n
\n
\n\n\n
\n We have studied the effect of weak randomness on q-state Potts models for q\\textgreater4 by measuring the central charges of these models using transfer matrix methods. We obtain a set of new values for the central charges and then show that some of these values are related to one another by a factorization law.\n
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\n \n\n \n \n \n \n \n \n A note on consistent anomalies.\n \n \n \n \n\n\n \n Baulieu, L.; Laroche, C.; Picco, M.; and Ohta, N.\n\n\n \n\n\n\n Physics Letters B, 414(1-2): 77–84. nov 1997.\n \n\n\n\n
\n\n\n\n \n \n \"APaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
\n
@article{Baulieu1997,\nabstract = {Within a BRST formulation, we determine the expressions of the consistent anomaly for superstrings with extended worldsheet supersymmetries of rank N. We consider the O(N) superconformal algebras up to N=4, as well as the `small N=4' superalgebra. This is done using a superfield formalism, allowing to recover previous results that were expressed in components. Moreover, we identify the `small N=4' algebra as the constrained `large N=4' via a self-duality like condition in superspace.},\narchivePrefix = {arXiv},\narxivId = {hep-th/9707256},\nauthor = {Baulieu, Laurent and Laroche, C{\\'{e}}line and Picco, Marco and Ohta, Nobuyoshi},\ndoi = {10.1016/S0370-2693(97)01134-9},\neprint = {9707256},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Baulieu et al. - 1997 - A note on consistent anomalies(2).pdf:pdf},\nissn = {03702693},\njournal = {Physics Letters B},\nmonth = {nov},\nnumber = {1-2},\npages = {77--84},\nprimaryClass = {hep-th},\ntitle = {{A note on consistent anomalies}},\nurl = {http://arxiv.org/abs/hep-th/9707256},\nvolume = {414},\nyear = {1997}\n}\n
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\n\n\n
\n Within a BRST formulation, we determine the expressions of the consistent anomaly for superstrings with extended worldsheet supersymmetries of rank N. We consider the O(N) superconformal algebras up to N=4, as well as the `small N=4' superalgebra. This is done using a superfield formalism, allowing to recover previous results that were expressed in components. Moreover, we identify the `small N=4' algebra as the constrained `large N=4' via a self-duality like condition in superspace.\n
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\n  \n 1996\n \n \n (2)\n \n \n
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\n \n\n \n \n \n \n \n \n Numerical results for the two-dimensional random-bond three-state Potts model.\n \n \n \n \n\n\n \n Picco, M.\n\n\n \n\n\n\n Physical Review B, 54(21): 14930–14933. dec 1996.\n \n\n\n\n
\n\n\n\n \n \n \"NumericalPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Picco1996,\nabstract = {We present results of a numerical simulation of the 3-state Potts model with random bond, in two dimension. In particular, we measure the critical exponent associated to the magnetization and the specific heat. We also compare these exponents with recent analytical computations.},\narchivePrefix = {arXiv},\narxivId = {cond-mat/9507025},\nauthor = {Picco, Marco},\ndoi = {10.1103/PhysRevB.54.14930},\neprint = {9507025},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Picco - 1996 - Numerical results for the two-dimensional random-bond three-state Potts model(3).pdf:pdf},\nissn = {0163-1829},\njournal = {Physical Review B},\nmonth = {dec},\nnumber = {21},\npages = {14930--14933},\nprimaryClass = {cond-mat},\ntitle = {{Numerical results for the two-dimensional random-bond three-state Potts model}},\nurl = {http://arxiv.org/abs/cond-mat/9507025 https://link.aps.org/doi/10.1103/PhysRevB.54.14930},\nvolume = {54},\nyear = {1996}\n}\n
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\n\n\n
\n We present results of a numerical simulation of the 3-state Potts model with random bond, in two dimension. In particular, we measure the critical exponent associated to the magnetization and the specific heat. We also compare these exponents with recent analytical computations.\n
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\n \n\n \n \n \n \n \n \n Randomly coupled minimal models.\n \n \n \n \n\n\n \n Dotsenko, V.; Picco, M.; and Pujol, P.\n\n\n \n\n\n\n Physics Letters B, 383(3): 287–293. sep 1996.\n \n\n\n\n
\n\n\n\n \n \n \"RandomlyPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
\n
@article{Dotsenko1996,\nabstract = {Using 1-loop renormalisation group equations, we analyze the effect of randomness on multi-critical unitary minimal conformal models. We study the case of two randomly coupled {\\$}M{\\_}p{\\$} models and found that they flow in two decoupled {\\$}M{\\_}{\\{}p-1{\\}}{\\$} models, in the infra-red limit. This result is then extend to the case with {\\$}M{\\$} randomly coupled {\\$}M{\\_}p{\\$} models, which will flow toward {\\$}M{\\$} decoupled {\\$}M{\\_}{\\{}p-1{\\}}{\\$}.},\narchivePrefix = {arXiv},\narxivId = {hep-th/9512087},\nauthor = {Dotsenko, Vladimir and Picco, Marco and Pujol, Pierre},\ndoi = {10.1016/0370-2693(96)00759-9},\neprint = {9512087},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Dotsenko, Picco, Pujol - 1996 - Randomly coupled minimal models(2).pdf:pdf},\nissn = {03702693},\njournal = {Physics Letters B},\nmonth = {sep},\nnumber = {3},\npages = {287--293},\nprimaryClass = {hep-th},\ntitle = {{Randomly coupled minimal models}},\nurl = {http://arxiv.org/abs/hep-th/9512087},\nvolume = {383},\nyear = {1996}\n}\n
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\n Using 1-loop renormalisation group equations, we analyze the effect of randomness on multi-critical unitary minimal conformal models. We study the case of two randomly coupled $}M{_}p{$ models and found that they flow in two decoupled $}M{_}{\\{}p-1{\\}}{$ models, in the infra-red limit. This result is then extend to the case with $}M{$ randomly coupled $}M{_}p{$ models, which will flow toward $}M{$ decoupled $}M{_}{\\{}p-1{\\}}{$.\n
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\n  \n 1995\n \n \n (5)\n \n \n
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\n \n\n \n \n \n \n \n \n Self-avoiding surfaces in the 3d Ising model.\n \n \n \n \n\n\n \n Dotsenko, V. V.; Picco, M.; Windey, P.; Harris, G.; Martinec, E.; and Marinari, E.\n\n\n \n\n\n\n Nuclear Physics B, 488(3): 577. 1995.\n \n\n\n\n
\n\n\n\n \n \n \"Self-avoidingPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Dotsenko1995d,\nabstract = {We examine the geometrical and topological properties of surfaces surrounding clusters in the 3d Ising model. For geometrical clusters at the percolation temperature and Fortuin-Kasteleyn clusters at T c , the number of surfaces of genus g and area A behaves as A x(g)  e -$\\mu$(g)A , with x approximately linear in g and $\\mu$ constant. These scaling laws are the same as those we obtain for simulations of 3d bond percolation. We observe that cross sections of spin domain boundaries at T c  decompose into a distribution N(l) of loops of length l that scales as l -$\\tau$  with $\\tau$ ∼ 2.2. We also present some new numerical results for 2d self-avoiding loops that we compare with analytic predictions. We address the prospects for a string-theoretic description of cluster boundaries. {\\textcopyright} 1995.},\nauthor = {Dotsenko, V.S. VS and Picco, M. and Windey, P. and Harris, G. and Martinec, E. and Marinari, E.},\ndoi = {10.1016/0550-3213(95)00278-Z},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Dotsenko et al. - 1995 - Self-avoiding surfaces in the 3d Ising model(2).pdf:pdf},\nissn = {05503213},\njournal = {Nuclear Physics B},\nnumber = {3},\npages = {577},\ntitle = {{Self-avoiding surfaces in the 3d Ising model}},\nurl = {http://www.sciencedirect.com/science/article/pii/055032139500278Z},\nvolume = {488},\nyear = {1995}\n}\n
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\n We examine the geometrical and topological properties of surfaces surrounding clusters in the 3d Ising model. For geometrical clusters at the percolation temperature and Fortuin-Kasteleyn clusters at T c , the number of surfaces of genus g and area A behaves as A x(g) e -$μ$(g)A , with x approximately linear in g and $μ$ constant. These scaling laws are the same as those we obtain for simulations of 3d bond percolation. We observe that cross sections of spin domain boundaries at T c decompose into a distribution N(l) of loops of length l that scales as l -$τ$ with $τ$ ∼ 2.2. We also present some new numerical results for 2d self-avoiding loops that we compare with analytic predictions. We address the prospects for a string-theoretic description of cluster boundaries. © 1995.\n
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\n \n\n \n \n \n \n \n \n Renormalisation-group calculation of correlation functions for the 2D random bond Ising and Potts models.\n \n \n \n \n\n\n \n Dotsenko, V.; Picco, M.; and Pujol, P.\n\n\n \n\n\n\n Nuclear Physics B, 455(3): 701–723. sep 1995.\n \n\n\n\n
\n\n\n\n \n \n \"Renormalisation-groupPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Dotsenko1995g,\nabstract = {We find the cross-over behavior for the spin-spin correlation function for the 2D Ising and 3-states Potts model with random bonds at the critical point. The procedure employed is the renormalisation approach of the perturbation series around the conformal field theories representing the pure models. We obtain a crossover in the amplitude for the correlation function for the Ising model which doesn't change the critical exponent, and a shift in the critical exponent produced by randomness in the case of the Potts model. A comparison with numerical data is discussed briefly.},\narchivePrefix = {arXiv},\narxivId = {hep-th/9501017},\nauthor = {Dotsenko, Vladimir and Picco, Marco and Pujol, Pierre},\ndoi = {10.1016/0550-3213(95)00534-Y},\neprint = {9501017},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Dotsenko, Picco, Pujol - 1995 - Renormalisation-group calculation of correlation functions for the 2D random bond Ising and Potts mod(7).pdf:pdf},\nissn = {05503213},\njournal = {Nuclear Physics B},\nmonth = {sep},\nnumber = {3},\npages = {701--723},\nprimaryClass = {hep-th},\ntitle = {{Renormalisation-group calculation of correlation functions for the 2D random bond Ising and Potts models}},\nurl = {http://arxiv.org/abs/hep-th/9501017},\nvolume = {455},\nyear = {1995}\n}\n
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\n We find the cross-over behavior for the spin-spin correlation function for the 2D Ising and 3-states Potts model with random bonds at the critical point. The procedure employed is the renormalisation approach of the perturbation series around the conformal field theories representing the pure models. We obtain a crossover in the amplitude for the correlation function for the Ising model which doesn't change the critical exponent, and a shift in the critical exponent produced by randomness in the case of the Potts model. A comparison with numerical data is discussed briefly.\n
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\n \n\n \n \n \n \n \n \n The Phenomenology of Strings and Clusters in the 3-d Ising Model.\n \n \n \n \n\n\n \n Dotsenko, V. S.; Picco, M.; Windey, P.; Lpthe; Harris, G.; Marinari, E.; and Martinec, E.\n\n\n \n\n\n\n In arXiv preprint hep-th/ …, pages 99–117. Jan 1995.\n \n\n\n\n
\n\n\n\n \n \n \"ThePaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@incollection{Dotsenko1994a,\nabstract = {We examine the geometrical and topological properties of surfaces surrounding clusters in the 3--{\\$}d{\\$} Ising model. For geometrical clusters at the percolation temperature and Fortuin--Kasteleyn clusters at {\\$}T{\\_}c{\\$}, the number of surfaces of genus {\\$}g{\\$} and area {\\$}A{\\$} behaves as {\\$}A{\\^{}}{\\{}x(g){\\}}e{\\^{}}{\\{}-\\backslashmu(g)A{\\}}{\\$}, with {\\$}x{\\$} approximately linear in {\\$}g{\\$} and {\\$}\\backslashmu{\\$} constant. We observe that cross--sections of spin domain boundaries at {\\$}T{\\_}c{\\$} decompose into a distribution {\\$}N(l){\\$} of loops of length {\\$}l{\\$} that scales as {\\$}l{\\^{}}{\\{}-\\backslashtau{\\}}{\\$} with {\\$}\\backslashtau \\backslashsim 2.2{\\$}. We address the prospects for a string--theoretic description of cluster boundaries. (To appear in proceedings for the Cargese Workshop on "String Theory, Conformal Models and Topological Field Theories", May 1993)},\narchivePrefix = {arXiv},\narxivId = {hep-th/9401129},\nauthor = {Dotsenko, Vladimir S. and Picco, Marco and Windey, Paul and Lpthe and Harris, Geoffrey and Marinari, Enzo and Martinec, Emil},\nbooktitle = {arXiv preprint hep-th/ {\\ldots}},\ndoi = {10.1007/978-1-4615-1819-8_9},\neprint = {9401129},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Dotsenko, Picco, Windey - 1993 - The Phenomenology of Strings and Clusters in the 3 – d Ising Model.pdf:pdf},\nmonth = {jan},\nnumber = {l},\npages = {99--117},\nprimaryClass = {hep-th},\ntitle = {{The Phenomenology of Strings and Clusters in the 3-d Ising Model}},\nurl = {http://arxiv.org/abs/hep-th/9401129 https://doi.org/10.1007/978-1-4615-1819-8{\\_}9 http://link.springer.com/10.1007/978-1-4615-1819-8{\\_}9},\nyear = {1995}\n}\n
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\n We examine the geometrical and topological properties of surfaces surrounding clusters in the 3–$}d{$ Ising model. For geometrical clusters at the percolation temperature and Fortuin–Kasteleyn clusters at $}T{_}c{$, the number of surfaces of genus $}g{$ and area $}A{$ behaves as $}A{^}{\\{}x(g){\\}}e{^}{\\{}-\\mu(g)A{\\}}{$, with $}x{$ approximately linear in $}g{$ and $}\\mu{$ constant. We observe that cross–sections of spin domain boundaries at $}T{_}c{$ decompose into a distribution $}N(l){$ of loops of length $}l{$ that scales as $}l{^}{\\{}-\\tau{\\}}{$ with $}\\tau \\sim 2.2{$. We address the prospects for a string–theoretic description of cluster boundaries. (To appear in proceedings for the Cargese Workshop on \"String Theory, Conformal Models and Topological Field Theories\", May 1993)\n
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\n \n\n \n \n \n \n \n \n Renormalization Group Solution for the Two-Dimensional Random Bond Potts Model with Broken Replica Symmetry.\n \n \n \n \n\n\n \n Dotsenko, V. S; Dotsenko, V. S; Picco, M.; and Pujol, P.\n\n\n \n\n\n\n Europhysics Letters (EPL), 32(5): 425–429. nov 1995.\n \n\n\n\n
\n\n\n\n \n \n \"RenormalizationPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Dotsenko1995,\nabstract = {We find a new solution of the renormalization group for the Potts model with ferromagnetic random valued coupling constants. The solution exhibits universality and broken replica symmetry. It is argued that the model reaches this universality class if the replica symmetry is broken initially. Otherwise the model stays with the replica symmetric renormalization group flow and reaches the fixed point which has been considered before.},\narchivePrefix = {arXiv},\narxivId = {hep-th/9502134},\nauthor = {Dotsenko, Vik S and Dotsenko, Vl S and Picco, M. and Pujol, P.},\ndoi = {10.1209/0295-5075/32/5/008},\neprint = {9502134},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Dotsenko et al. - 1995 - Renormalization Group Solution for the Two-Dimensional Random Bond Potts Model with Broken Replica Symmetry.pdf:pdf},\nissn = {0295-5075},\njournal = {Europhysics Letters (EPL)},\nmonth = {nov},\nnumber = {5},\npages = {425--429},\nprimaryClass = {hep-th},\ntitle = {{Renormalization Group Solution for the Two-Dimensional Random Bond Potts Model with Broken Replica Symmetry}},\nurl = {http://arxiv.org/abs/hep-th/9502134 http://stacks.iop.org/0295-5075/32/i=5/a=008?key=crossref.270aad982b2a9dbce70d5227d708b0e9},\nvolume = {32},\nyear = {1995}\n}\n
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\n We find a new solution of the renormalization group for the Potts model with ferromagnetic random valued coupling constants. The solution exhibits universality and broken replica symmetry. It is argued that the model reaches this universality class if the replica symmetry is broken initially. Otherwise the model stays with the replica symmetric renormalization group flow and reaches the fixed point which has been considered before.\n
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\n \n\n \n \n \n \n \n \n Correlation functions for the 2D random bonds Potts Models.\n \n \n \n \n\n\n \n Dotsenko, V.; Picco, M.; and Pujol, P.\n\n\n \n\n\n\n Nuclear Physics B, 5632: 145–153. sep 1995.\n \n\n\n\n
\n\n\n\n \n \n \"CorrelationPaper\n  \n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Dotsenko1995b,\nabstract = {We study the spin-spin and energy-energy correlation functions for the 2D Ising and 3-states Potts model with random bonds at the critical point. The procedure employed is the renormalisation group approach of the perturbation series around the conformal field theories representing the pure models. For the Ising model, we obtain a crossover in the amplitude for the correlation functions which doesn't change the critical exponent. For the {\\$}3{\\$}-state Potts model, we found a shift in the critical exponent produced by randomness. A comparison with numerical data is discussed briefly.},\narchivePrefix = {arXiv},\narxivId = {cond-mat/9509149},\nauthor = {Dotsenko, Vladimir and Picco, Marco and Pujol, Pierre},\neprint = {9509149},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Dotsenko, Picco, Pujol - 1995 - Renormalisation-group calculation of correlation functions for the 2D random bond Ising and Potts mod(5).pdf:pdf},\njournal = {Nuclear Physics B},\nmonth = {sep},\npages = {145--153},\nprimaryClass = {cond-mat},\ntitle = {{Correlation functions for the 2D random bonds Potts Models}},\nurl = {http://arxiv.org/abs/cond-mat/9509149},\nvolume = {5632},\nyear = {1995}\n}\n
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\n\n\n
\n We study the spin-spin and energy-energy correlation functions for the 2D Ising and 3-states Potts model with random bonds at the critical point. The procedure employed is the renormalisation group approach of the perturbation series around the conformal field theories representing the pure models. For the Ising model, we obtain a crossover in the amplitude for the correlation functions which doesn't change the critical exponent. For the $}3{$-state Potts model, we found a shift in the critical exponent produced by randomness. A comparison with numerical data is discussed briefly.\n
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\n  \n 1994\n \n \n (2)\n \n \n
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\n \n\n \n \n \n \n \n \n Numerical study of the Ising spin glass in a magnetic field.\n \n \n \n \n\n\n \n Picco, M.; and Ritort, F.\n\n\n \n\n\n\n Journal de Physique I, 4(11): 1619–1625. nov 1994.\n \n\n\n\n
\n\n\n\n \n \n \"NumericalPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Picco1994,\nabstract = {We study the order parameter distribution P(q) in the 4d Ising spin glass with {\\$}\\backslashpm J{\\$} couplings in a magnetic field. We also compare these results with simulations for the infinite ranged model (i.e. SK model.) Then we analyse our numerical results in the framework of the droplet picture as well as in the mean field approach.},\narchivePrefix = {arXiv},\narxivId = {cond-mat/9403077},\nauthor = {Picco, Marco and Ritort, Felix},\ndoi = {10.1051/jp1:1994114},\neprint = {9403077},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Picco, Ritort - 1994 - Numerical study of the Ising spin glass in a magnetic field(2).pdf:pdf},\nissn = {1155-4304},\njournal = {Journal de Physique I},\nmonth = {nov},\nnumber = {11},\npages = {1619--1625},\nprimaryClass = {cond-mat},\ntitle = {{Numerical study of the Ising spin glass in a magnetic field}},\nurl = {http://arxiv.org/abs/cond-mat/9403077 http://www.edpsciences.org/10.1051/jp1:1994114},\nvolume = {4},\nyear = {1994}\n}\n
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\n We study the order parameter distribution P(q) in the 4d Ising spin glass with $}\\pm J{$ couplings in a magnetic field. We also compare these results with simulations for the infinite ranged model (i.e. SK model.) Then we analyse our numerical results in the framework of the droplet picture as well as in the mean field approach.\n
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\n \n\n \n \n \n \n \n \n Spin–spin critical point correlation functions for the 2D random bond Ising and Potts models.\n \n \n \n \n\n\n \n Dotsenko, V.; Picco, M.; and Pujol, P.\n\n\n \n\n\n\n Physics Letters B, 347(280): 113–119. 1994.\n \n\n\n\n
\n\n\n\n \n \n \"Spin–spinPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Dotsenko1994,\nabstract = {We compute the combined two and three loop order correction to the spin-spin correlation functions for the 2D Ising and q-states Potts model with random bonds at the critical point. The procedure employed is the renormalisation group approach for the perturbation series around the conformal field theories representing the pure models. We obtain corrections for the correlations functions which produce crossover in the amplitude but don't change the critical exponent in the case of the Ising model and which produce a shift in the critical exponent, due to randomness, in the case of the Potts model. Comparison with numerical data is discussed briefly.},\narchivePrefix = {arXiv},\narxivId = {hep-th/9405003},\nauthor = {Dotsenko, Vladimir and Picco, Marco and Pujol, Pierre},\ndoi = {10.1016/0370-2693(95)00035-J},\neprint = {9405003},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Dotsenko, Picco, Pujol - 1994 - Spin--spin critical point correlation functions for the 2D random bond Ising and Potts models(3).pdf:pdf},\nissn = {03702693},\njournal = {Physics Letters B},\nnumber = {280},\npages = {113--119},\nprimaryClass = {hep-th},\ntitle = {{Spin--spin critical point correlation functions for the 2D random bond Ising and Potts models}},\nurl = {http://arxiv.org/abs/hep-th/9405003},\nvolume = {347},\nyear = {1994}\n}\n
\n
\n\n\n
\n We compute the combined two and three loop order correction to the spin-spin correlation functions for the 2D Ising and q-states Potts model with random bonds at the critical point. The procedure employed is the renormalisation group approach for the perturbation series around the conformal field theories representing the pure models. We obtain corrections for the correlations functions which produce crossover in the amplitude but don't change the critical exponent in the case of the Ising model and which produce a shift in the critical exponent, due to randomness, in the case of the Potts model. Comparison with numerical data is discussed briefly.\n
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\n  \n 1993\n \n \n (1)\n \n \n
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\n \n\n \n \n \n \n \n \n Critical and topological properties of cluster boundaries in the 3D Ising model.\n \n \n \n \n\n\n \n Dotsenko, V. S.; Windey, P.; Harris, G.; Marinari, E.; Martinec, E.; and Picco, M.\n\n\n \n\n\n\n Physical Review Letters, 71(6): 811–814. aug 1993.\n \n\n\n\n
\n\n\n\n \n \n \"CriticalPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Dotsenko1993,\nabstract = {We analyze the ensemble of surfaces surrounding critical clusters at T=Tc in the 3D Ising model. We find that Ng(A), the number of surfaces of genus g and area A, behaves as Ax(g)e-$\\mu$A. We show that $\\mu$ is constant and x(g) is approximately linear; the sum tsumg Ng(A) scales as a power of A. The cluster volume is proportional to its surface area. We discuss similar reuslts for the ordinary spin clusters of the 3D Ising model and for 3D bond percolation.},\nauthor = {Dotsenko, Vladimir S. and Windey, Paul and Harris, Geoffrey and Marinari, Enzo and Martinec, Emil and Picco, Marco},\ndoi = {10.1103/PhysRevLett.71.811},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Dotsenko et al. - 1993 - Critical and topological properties of cluster boundaries in the 3D Ising model.pdf:pdf},\nissn = {0031-9007},\njournal = {Physical Review Letters},\nmonth = {aug},\nnumber = {6},\npages = {811--814},\npublisher = {American Physical Society},\nshorttitle = {Phys. Rev. Lett.},\ntitle = {{Critical and topological properties of cluster boundaries in the 3D Ising model}},\nurl = {http://link.aps.org/doi/10.1103/PhysRevLett.71.811 https://link.aps.org/doi/10.1103/PhysRevLett.71.811},\nvolume = {71},\nyear = {1993}\n}\n
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\n We analyze the ensemble of surfaces surrounding critical clusters at T=Tc in the 3D Ising model. We find that Ng(A), the number of surfaces of genus g and area A, behaves as Ax(g)e-$μ$A. We show that $μ$ is constant and x(g) is approximately linear; the sum tsumg Ng(A) scales as a power of A. The cluster volume is proportional to its surface area. We discuss similar reuslts for the ordinary spin clusters of the 3D Ising model and for 3D bond percolation.\n
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\n  \n 1992\n \n \n (1)\n \n \n
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\n \n\n \n \n \n \n \n \n Modeles de matrices et gravite quantique bidimensionnelle.\n \n \n \n \n\n\n \n PICCO, M.\n\n\n \n\n\n\n Ph.D. Thesis, jan 1992.\n \n\n\n\n
\n\n\n\n \n \n \"ModelesPaper\n  \n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n\n \n  \n \n 1 download\n \n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n\n\n\n
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@phdthesis{PICCO1992,\nauthor = {PICCO, MARCO},\nbooktitle = {http://www.theses.fr},\nkeywords = {en fran{\\c{c}}ais},\nmonth = {jan},\npublisher = {Paris 11},\ntitle = {{Modeles de matrices et gravite quantique bidimensionnelle}},\nurl = {http://www.theses.fr/1992PA112049},\nyear = {1992}\n}\n
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\n  \n 1991\n \n \n (2)\n \n \n
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\n \n\n \n \n \n \n \n \n SL(n, ) topological field theories.\n \n \n \n \n\n\n \n Baulieu, L.; and Picco, M.\n\n\n \n\n\n\n Physics Letters B, 254(3-4): 391–400. jan 1991.\n \n\n\n\n
\n\n\n\n \n \n \"SL(n,Paper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Baulieu1991,\nabstract = {We detail the BRST quantization of zero-dimensional string theory, by using Singer's observation of a SL(2, R) gauge symmetry. This provides a supersymmetric action, involving a pair of fermions and a pair of bosons. This confirms Singer's result that the partition function is a ratio of determinants. We generalize our result, and show that the quantization of the purely cosmological action ∫dnxg in arbitrary dimensions n is based on a gauge symmetry of the topological type, stemming from the SL(n, R) and diffeomorphism invariances of ∫dnxg. The corresponding supersymmetric action depends on a tower of one-form, two-form up to n-form commuting and anticommuting gauge fields, and should induce a topological quantum theory. The partition function does not reduce to a product of ratios of determinants for n{\\textgreater}2. For n=2, the coupling to matter is manageable, without breaking the topological invariance, by addition of a topological $\\sigma$-model, suitably gauge fixed in a BRST invariant way.},\nauthor = {Baulieu, Laurent and Picco, Marco},\ndoi = {10.1016/0370-2693(91)91174-T},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Baulieu, Picco - 1991 - SL(n, ) topological field theories.pdf:pdf},\nissn = {03702693},\njournal = {Physics Letters B},\nmonth = {jan},\nnumber = {3-4},\npages = {391--400},\npublisher = {North-Holland},\ntitle = {{SL(n, ) topological field theories}},\nurl = {https://linkinghub.elsevier.com/retrieve/pii/037026939191174T},\nvolume = {254},\nyear = {1991}\n}\n
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\n We detail the BRST quantization of zero-dimensional string theory, by using Singer's observation of a SL(2, R) gauge symmetry. This provides a supersymmetric action, involving a pair of fermions and a pair of bosons. This confirms Singer's result that the partition function is a ratio of determinants. We generalize our result, and show that the quantization of the purely cosmological action ∫dnxg in arbitrary dimensions n is based on a gauge symmetry of the topological type, stemming from the SL(n, R) and diffeomorphism invariances of ∫dnxg. The corresponding supersymmetric action depends on a tower of one-form, two-form up to n-form commuting and anticommuting gauge fields, and should induce a topological quantum theory. The partition function does not reduce to a product of ratios of determinants for n\\textgreater2. For n=2, the coupling to matter is manageable, without breaking the topological invariance, by addition of a topological $σ$-model, suitably gauge fixed in a BRST invariant way.\n
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\n \n\n \n \n \n \n \n \n SUSCEPTIBILITY FOR 2-d GRAVITY COUPLED TO SO(2,1) BF SYSTEM.\n \n \n \n \n\n\n \n Picco, M.; and Wallet, J.\n\n\n \n\n\n\n Modern Physics Letters A, 06(32): 2965–2972. oct 1991.\n \n\n\n\n
\n\n\n\n \n \n \"SUSCEPTIBILITYPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Picco1991,\nabstract = {We consider two-dimensional gravity in the presence of a system of fields described by an action which can be derived from a topological theory with gauge group SO(2,1). Working in the continuum approach, we extract the area dependence of the partition function and deduce the susceptibility for the theory. The inclusion of D massless scalars gives a susceptibility depending linearly on D. We finally discuss our results.},\nauthor = {Picco, Marco and Wallet, Jean-Christophe},\ndoi = {10.1142/S0217732391003468},\nissn = {0217-7323},\njournal = {Modern Physics Letters A},\nlanguage = {en},\nmonth = {oct},\nnumber = {32},\npages = {2965--2972},\npublisher = {World Scientific Publishing Company},\ntitle = {{SUSCEPTIBILITY FOR 2-d GRAVITY COUPLED TO SO(2,1) BF SYSTEM}},\nurl = {http://www.worldscientific.com/doi/abs/10.1142/S0217732391003468{\\#}.WFAD5MZDPjc.mendeley},\nvolume = {06},\nyear = {1991}\n}\n
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\n We consider two-dimensional gravity in the presence of a system of fields described by an action which can be derived from a topological theory with gauge group SO(2,1). Working in the continuum approach, we extract the area dependence of the partition function and deduce the susceptibility for the theory. The inclusion of D massless scalars gives a susceptibility depending linearly on D. We finally discuss our results.\n
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\n  \n 1990\n \n \n (2)\n \n \n
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\n \n\n \n \n \n \n \n \n Non-perturbative interpretation of the phase structure of unitary matrix models.\n \n \n \n \n\n\n \n Houart, L.; and Picco, M.\n\n\n \n\n\n\n Physics Letters B, 252(3): 395–400. dec 1990.\n \n\n\n\n
\n\n\n\n \n \n \"Non-perturbativePaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Houart1990,\nabstract = {We analyze in detail the phase diagram of a unitary matrix model. We show that there are connections between the phase boundaries and the different types of string equations obtained with the orthogonal polynomial method.},\nauthor = {Houart, Laurent and Picco, Marco},\ndoi = {10.1016/0370-2693(90)90558-N},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Houart, Picco - 1990 - Non-perturbative interpretation of the phase structure of unitary matrix models(3).pdf:pdf},\nissn = {03702693},\njournal = {Physics Letters B},\nmonth = {dec},\nnumber = {3},\npages = {395--400},\npublisher = {North-Holland},\ntitle = {{Non-perturbative interpretation of the phase structure of unitary matrix models}},\nurl = {http://linkinghub.elsevier.com/retrieve/pii/037026939090558N},\nvolume = {252},\nyear = {1990}\n}\n
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\n We analyze in detail the phase diagram of a unitary matrix model. We show that there are connections between the phase boundaries and the different types of string equations obtained with the orthogonal polynomial method.\n
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\n \n\n \n \n \n \n \n \n Stochastic quantization of 2D gravity and its link with 3D gravity and topological 4D gravity.\n \n \n \n \n\n\n \n Baulieu, L.; Bilal, A.; and Picco, M.\n\n\n \n\n\n\n Nuclear Physics B, 346(2-3): 507–526. dec 1990.\n \n\n\n\n
\n\n\n\n \n \n \"StochasticPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{Baulieu1990,\nabstract = {We apply stochastic quantization to two-dimensional gravity. The Laplace operator acting on the space of all metrics takes a particularly simple form in terms of the Beltrami parametrization. We show the equivalence between the quantum theory defined by the standard Faddeev-Popov gauge fixing of the two-dimensional diffeomorphism invariance and the one defined by stochastic quantization. We do so by using the gauge freedom left in the Langevin equation of a diffeomorphism-invariant theory to adjust the drift force. Another choice of the drift force, comparable to that of Zwanziger for Yang-Mills theories, seems to avoid the analogue of the Gribov ambiguity, i.e. the necessity of the by-hand restriction to one fundamental domain. We relate the two-dimensional gravity to a three-dimensional theory, based on the three-dimensional gravitational Chern-Simons action for SL(2, C), ISO(3) or SU(2) × SU(2) (depending on the genus of the two-dimensional Riemann surface), in which all fields of the stochastic quantization have been distributed as components of the gauge fields. To study the three-dimensional theory, stochastic quantization can be applied once more. This gives a theory with the action of topological gravity in four dimensions, namely the Pontrjagin invariant ∫N2×R×R tr R ∧ R, gauge fixed by self-duality conditions.},\nauthor = {Baulieu, Laurent and Bilal, Adel and Picco, Marco},\ndoi = {10.1016/0550-3213(90)90290-T},\nfile = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Baulieu, Bilal, Picco - 1990 - Stochastic quantization of 2D gravity and its link with 3D gravity and topological 4D gravity(2).pdf:pdf},\nissn = {05503213},\njournal = {Nuclear Physics B},\nmonth = {dec},\nnumber = {2-3},\npages = {507--526},\npublisher = {North-Holland},\ntitle = {{Stochastic quantization of 2D gravity and its link with 3D gravity and topological 4D gravity}},\nurl = {https://linkinghub.elsevier.com/retrieve/pii/055032139090290T},\nvolume = {346},\nyear = {1990}\n}\n
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\n We apply stochastic quantization to two-dimensional gravity. The Laplace operator acting on the space of all metrics takes a particularly simple form in terms of the Beltrami parametrization. We show the equivalence between the quantum theory defined by the standard Faddeev-Popov gauge fixing of the two-dimensional diffeomorphism invariance and the one defined by stochastic quantization. We do so by using the gauge freedom left in the Langevin equation of a diffeomorphism-invariant theory to adjust the drift force. Another choice of the drift force, comparable to that of Zwanziger for Yang-Mills theories, seems to avoid the analogue of the Gribov ambiguity, i.e. the necessity of the by-hand restriction to one fundamental domain. We relate the two-dimensional gravity to a three-dimensional theory, based on the three-dimensional gravitational Chern-Simons action for SL(2, C), ISO(3) or SU(2) × SU(2) (depending on the genus of the two-dimensional Riemann surface), in which all fields of the stochastic quantization have been distributed as components of the gauge fields. To study the three-dimensional theory, stochastic quantization can be applied once more. This gives a theory with the action of topological gravity in four dimensions, namely the Pontrjagin invariant ∫N2×R×R tr R ∧ R, gauge fixed by self-duality conditions.\n
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@article{Picco2019,\nabstract = {We perform Monte-Carlo computations of four-point cluster connectivities in the critical 2d Potts model, for numbers of states Q$\\backslash$in (0,4) Q ∈ ( 0 , 4 ) that are not necessarily integer. We compare these connectivities to four-point functions in a CFT that interpolates between D-series minimal models. We find that 3 combinations of the 4 independent connectivities agree with CFT four-point functions, down to the 2 2 to 4 4 significant digits of our Monte-Carlo computations. However, we argue that the agreement is exact only in the special cases Q=0, 3, 4 Q = 0 , 3 , 4 . We conjecture that the Potts model can be analytically continued to a double cover of the half-plane $\\backslash${\\{}$\\backslash$Re c {\\{} ℜ c {\\textless} 13 {\\}} , where c c is the central charge of the Virasoro symmetry algebra.}}
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\n We perform Monte-Carlo computations of four-point cluster connectivities in the critical 2d Potts model, for numbers of states Q$\\$in (0,4) Q ∈ ( 0 , 4 ) that are not necessarily integer. We compare these connectivities to four-point functions in a CFT that interpolates between D-series minimal models. We find that 3 combinations of the 4 independent connectivities agree with CFT four-point functions, down to the 2 2 to 4 4 significant digits of our Monte-Carlo computations. However, we argue that the agreement is exact only in the special cases Q=0, 3, 4 Q = 0 , 3 , 4 . We conjecture that the Potts model can be analytically continued to a double cover of the half-plane $\\$\\$\\$Re c \\ ℜ c \\textless 13 \\ , where c c is the central charge of the Virasoro symmetry algebra.\n
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