Self-avoiding surfaces in the 3d Ising model. Dotsenko, V. V.; Picco, M.; Windey, P.; Harris, G.; Martinec, E.; and Marinari, E. Nuclear Physics B, 488(3):577, 1995.
Self-avoiding surfaces in the 3d Ising model [link]Paper  doi  abstract   bibtex   
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.
@article{Dotsenko1995d,
abstract = {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.},
author = {Dotsenko, V.S. VS and Picco, M. and Windey, P. and Harris, G. and Martinec, E. and Marinari, E.},
doi = {10.1016/0550-3213(95)00278-Z},
file = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Dotsenko et al. - 1995 - Self-avoiding surfaces in the 3d Ising model(2).pdf:pdf},
issn = {05503213},
journal = {Nuclear Physics B},
number = {3},
pages = {577},
title = {{Self-avoiding surfaces in the 3d Ising model}},
url = {http://www.sciencedirect.com/science/article/pii/055032139500278Z},
volume = {488},
year = {1995}
}
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