Monte Carlo Simulation of Magnetic System in the Tsallis Statistics

TL;DR

This paper demonstrates that the Broad Histogram Method is an efficient simulation tool for the Ising model within Tsallis statistics, revealing that phase transitions occur only at the extensive case where q=1.

Contribution

It introduces the application of the Broad Histogram Method to the Ising model under Tsallis statistics, providing new insights into phase transition behavior for different q values.

Findings

Phase transitions occur only at q=1 in the 2D Ising model.

The Broad Histogram Method is effective for non-extensive statistics.

Results suggest non-extensive systems do not exhibit finite-temperature phase transitions.

Abstract

We apply the Broad Histogram Method to an Ising system in the context of the recently reformulated Generalized Thermostatistics, and we claim it to be a very efficient simulation tool for this non-extensive statistics. Results are obtained for the nearest-neighbour version of the Ising model for a range of values of the $q$ parameter of Generalized Thermostatistics. We found an evidence that the 2D-Ising model does not undergo phase transitions at finite temperatures except for the extensive case $q=1$.