Strong disorder fixed points in the two-dimensional random-bond Ising model. , Honecker, A., & Pujol, P. Journal of Statistical Mechanics: Theory and Experiment, 2006(09):P09006–P09006, sep, 2006.
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.
@article{Picco2006,
abstract = {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.},
archivePrefix = {arXiv},
arxivId = {cond-mat/0606312},
author = {Picco, Marco and Honecker, Andreas and Pujol, Pierre},
doi = {10.1088/1742-5468/2006/09/P09006},
eprint = {0606312},
file = {: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},
issn = {1742-5468},
journal = {Journal of Statistical Mechanics: Theory and Experiment},
keywords = {Classical phase transitions (theory),Conformal field theory (theory),Disordered systems (theory),Renormalization group},
month = {sep},
number = {09},
pages = {P09006--P09006},
primaryClass = {cond-mat},
title = {{Strong disorder fixed points in the two-dimensional random-bond Ising model}},
url = {http://arxiv.org/abs/cond-mat/0606312 http://stacks.iop.org/1742-5468/2006/i=09/a=P09006?key=crossref.42340f86308ee12f1b2817bbb64ceb04},
volume = {2006},
year = {2006}
}