2004/02/29 by Oleg A. Vasilyev · 1 citation
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.72.036115
20 pages, 7 figures, v3:one fitting procedure is changed, grammatical changes
arxiv created 2005/03/21 · openalex publication_date 2005/09/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The scaling of the tails of the probability of a system to percolate only in the horizontal direction \ensuremathπhs was investigated numerically for the correlated site-bond percolation model (q-state Potts model) for q=1, 2, 3, 4 (where q is the number of spin states). We have to demonstrate that the crossing probability \ensuremathπhs(p) far from the critical point pc has the shape \ensuremathπhs(p)\ensuremath≃D\phantom\rule0.2em0exexp[cL(p\ensuremath-pc)^\ensuremathν] where \ensuremathν is the correlation length index, and p=1\ensuremath-exp(\ensuremath-\ensuremathβ) is the probability of a bond to be closed. For the tail region the correlation length is smaller than the lattice size. At criticality the correlation length reaches the sample size and we observe crossover to another scaling \ensuremathπhs(p)\ensuremath≃A\phantom\rule0.2em0exexp\ensuremath-b[L(p\ensuremath-pc)^\ensuremathν]x. Here x is a scaling index describing the central part of the crossing probability.