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

2000/05/25 by Oleg A. Vasilyev, O. A. Vasilyev, Vasilyev, O. A.
Mathematics · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech

paper · pdf · doi:10.48550/arxiv.cond-mat/0005452

12 pages, 7 eps-figures

arxiv created 2000/05/25 · openalex publication_date 2000/05/25 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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= \frac1ν for q<4. In contrast, y ≠ \frac1ν for q=4.

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