Scaling of crossing probabilities for the q-state Potts model at criticality

Abstract

We present study of finite-size scaling and universality of crossing probabilities for the $q$-state Potts model. Crossing probabilities of the Potts model are similar ones in percolation problem. We numerically investigated scaling of $π_{s}$ - the probability of a system to percolate only in one direction for two-dimensional site percolation, the Ising model, and the q-state Potts model for $q=3,4,5,6,8,10$. We found the thermal scaling index $y= \frac{1}ν$ for $q<4$. In contrast, $y \ne \frac{1}ν$ for $q=4$.