Simulation of the two-dimensional Potts model using nonextensive statistics

TL;DR

This paper explores the behavior of the two-dimensional Potts model within nonextensive statistical mechanics, using Monte Carlo simulations to analyze phase transitions and critical points under modified probability rules.

Contribution

It introduces a nonextensive framework to the Potts model and determines the nature and critical temperature of phase transitions in this context.

Findings

Potts model exhibits phase transition in nonextensive statistics

Order of the phase transition is established

Critical temperature varies with Tsallis entropic index

Abstract

The standard Potts model is investigated in the framework of nonextensive statistical mechanics. We performed Monte Carlo simulations on two-dimensional lattices with linear sizes ranging from 16 to 64 using the Metropolis algorithm, where the classical Boltzmann-Gibbs transition probabilities were modified for the nonextensive case. We found that the Potts model undergoes a phase transition in the nonextensive scenario. We established the order of the phase transition and we computed the critical temperature for different values of the Tsallis entropic index.