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

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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 πₛ - 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= 1ν for q<4. In contrast, y ≠ 1ν for q=4.