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

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

2000-05-25

arxiv.org/abs/cond-mat/0005452v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

12 pages, 7 eps-figures

Scientific paper

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 $\pi_{s}$ - 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 $y= \frac{1}{\nu}$ for $q<4$. In contrast, $y \ne \frac{1}{\nu}$ for $q=4$.

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