A Monte Carlo Method for the Numerical Simulation of Tsallis Statistics

TL;DR

This paper introduces a Monte Carlo simulation approach for Tsallis statistics, combining Metropolis algorithms with entropy integration to address numerical challenges, demonstrated on the 2d-Ising model.

Contribution

A novel Monte Carlo method that integrates entropy calculations to effectively simulate Tsallis statistics in complex systems.

Findings

Successfully applied to the 2d-Ising model

Overcomes numerical difficulties in Tsallis statistics simulation

Demonstrates effectiveness of combined Monte Carlo and entropy integration

Abstract

We present a new method devised to overcome the intrinsic difficulties associated to the numerical simulations of the Tsallis statistics. We use a standard Metropolis Monte Carlo algorithm at a fictitious temperature T', combined with a numerical integration method for the calculation of the entropy in order to evaluate the actual temperature T. We illustrate the method by applying it to the 2d-Ising model using a standard reweighting technique.