Tails of the crossing probability
Abstract
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 sitebond 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(pp_{c})^{ν}] where ν is the correlation length index, and p=1exp(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(pp_{c})^{ν}]^{x}} . Here x is a scaling index describing the central part of the crossing probability.
 Publication:

Physical Review E
 Pub Date:
 September 2005
 DOI:
 10.1103/PhysRevE.72.036115
 arXiv:
 arXiv:condmat/0402294
 Bibcode:
 2005PhRvE..72c6115V
 Keywords:

 05.50.+q;
 05.10.Ln;
 64.60.Ak;
 Lattice theory and statistics;
 Monte Carlo methods;
 Renormalizationgroup fractal and percolation studies of phase transitions;
 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Disordered Systems and Neural Networks
 EPrint:
 20 pages, 7 figures, v3:one fitting procedure is changed, grammatical changes