Critical and topological properties of cluster boundaries in the 3D Ising model. Dotsenko, V. S.; Windey, P.; Harris, G.; Marinari, E.; Martinec, E.; and Picco, M. Physical Review Letters, 71(6):811–814, American Physical Society, aug, 1993.
Critical and topological properties of cluster boundaries in the 3D Ising model [link]Paper  doi  abstract   bibtex   
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.
@article{Dotsenko1993,
abstract = {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.},
author = {Dotsenko, Vladimir S. and Windey, Paul and Harris, Geoffrey and Marinari, Enzo and Martinec, Emil and Picco, Marco},
doi = {10.1103/PhysRevLett.71.811},
file = {: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},
issn = {0031-9007},
journal = {Physical Review Letters},
month = {aug},
number = {6},
pages = {811--814},
publisher = {American Physical Society},
shorttitle = {Phys. Rev. Lett.},
title = {{Critical and topological properties of cluster boundaries in the 3D Ising model}},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.71.811 https://link.aps.org/doi/10.1103/PhysRevLett.71.811},
volume = {71},
year = {1993}
}
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