Tails of the crossing probability

The scaling of the tails of the probability of a system to percolate only in the horizontal direction π_hs 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 π_hs(p) far from the critical point p_c has the shape π_hs(p)≃Dexp[cL(p-p_c)^ν] where ν is the correlation length index, and p=1-exp(-β) 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 π_hs(p)≃Aexp{-b[L(p-p_c)^ν]^x} . Here x is a scaling index describing the central part of the crossing probability.