The Tails of the Crossing Probability

Details The Tails of the Crossing Probability The Tails of the Crossing Probability

2004-02-10

arxiv.org/abs/cond-mat/0402294v3

Physics

Condensed Matter

Statistical Mechanics

20 pages, 7 figures, v3:one fitting procedure is changed, grammatical changes

Scientific paper

10.1103/PhysRevE.72.036115

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 $\pi_{hs}(p) \simeq D \exp(c L[p-p_{c}]^{\nu})$ where $\nu$ is the correlation length index, $p=1-\exp(-\beta)$ is the probability of a bond to be closed. At criticality we observe crossover to another scaling $\pi_{hs}(p) \simeq A \exp (-b {L [p-p_{c}]^{\nu}}^{z})$. Here $z$ is a scaling index describing the central part of the crossing probability.

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