The Tails of the Crossing Probability

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 ${\pi }_{hs}(p)\simeq D\exp (cL[p-p_c{]}^{\nu })$ 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.

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

References in corpus (5)

• A fast Monte Carlo algorithm for site or bond percolation
• Convergence of threshold estimates for two-dimensional percolation
• Fractal geometry of critical Potts clusters
• Are the Tails of Percolation Thresholds Gaussians ?
• Universality of the Crossing Probability for the Potts Model for q=1,2,3,4

Cited by in corpus (1)

• Crossing probability and number of crossing clusters in off-critical percolation