The Tails of the Crossing Probability

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 $\pi_{hs}(p) \simeq A \exp (-b {L [p-p_{c}]^{\nu}}^{z})$\mathrm{.}Here$z$ is a scaling index describing the central part of the crossing probability.