Phase diagram of a 2D Ising model within a nonextensive approach

TL;DR

This paper explores the phase diagram of a 2D Ising model using a nonextensive statistical approach, revealing phase transitions influenced by the entropic parameter q and the Tsallis cutoff.

Contribution

It introduces a nonextensive Monte Carlo simulation of the 2D Ising model, demonstrating how the entropic parameter q affects phase transitions and magnetization states.

Findings

Phase transitions occur for q ≠ 1.

The q-phase diagram shows phases governed by q.

Tsallis cutoff is crucial for phase transition existence.

Abstract

In this work we report Monte Carlo simulations of a 2D Ising model, in which the statistics of the Metropolis algorithm is replaced by the nonextensive one. We compute the magnetization and show that phase transitions are present for $q\neq 1$. A $q -$ phase diagram (critical temperature vs. the entropic parameter $q$) is built and exhibits some interesting features, such as phases which are governed by the value of the entropic index $q$. It is shown that such phases favors some energy levels of magnetization states. It is also showed that the contribution of the Tsallis cutoff is essential to the existence of phase transitions.