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The Tails of the Crossing Probability | | Oleg A.Vasilyev
; | | Date: |
10 Feb 2004 | | Subject: | Statistical Mechanics; Disordered Systems and Neural Networks | cond-mat.stat-mech cond-mat.dis-nn | | Abstract: | The scaling of the tails of the probability of a system to percolate only in the horizontal direction $pi_{hs}$ was investigated numerically for correlated site-bond percolation model for $q=1,2,3,4$.We have to demonstrate that the tails of the crossing probability far from the critical point have shape $pi_{hs}(p) simeq D exp(c L[p-p_{c}]^{
u})$ where $
u$ is the correlation length index, $p=1-exp(-eta)$ is the probability of a bond to be closed. At criticality we observe crossover to another scaling $pi_{hs}(p) simeq A exp (-b {L [p-p_{c}]^{
u}}^{z})$. Here $z$ is a scaling index describing the central part of the crossing probability. | | Source: | arXiv, cond-mat/0402294 | | Services: | Forum | Review | PDF | Favorites | |
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