General method to perform Microcanonical Monte Carlo Simulations

TL;DR

This paper introduces a novel, ensemble-independent Monte Carlo method for microcanonical simulations using configurational temperature and stochastic dynamics, demonstrated on the 2D XY-model.

Contribution

The authors develop a new Monte Carlo approach for microcanonical ensemble simulations that is flexible and applicable with various update strategies, unlike traditional methods.

Findings

Successfully simulated the 2D XY-model in the microcanonical ensemble

Method is independent of the Monte Carlo update strategy

Demonstrated the method's effectiveness through numerical results

Abstract

Monte Carlo simulations have boosted the numerical study of several different physical systems and in particular, the canonical ensemble has been especially useful because of the existence of easy and efficient relaxation algorithms required to minimize the energy, the relevant extensive thermodynamic variable appearing in the probability distribution, which drives the system after a thermalization process to equilibrium. Nevertheless, the nature does not know about statistical ensembles and therefore it is desirable and a theoretical challenge to show how to perform efficient numerical simulations in the microcanonical ensemble. In this article, we present a method based on the concepts of configurational temperature estimator \cite{Rugh,GDP} and on stochastic dynamics to do it. The method is independent of the Monte Carlo update strategy, and can be implemented for both local update or cluster algorithms. We illustrate the main features of the method by performing a numerical simulation of the planar interacting classical spin system, known as the two-dimensional XY-model.