Extended canonical Monte Carlo methods: Improving accuracy of microcanonical calculations using a re-weighting technique

TL;DR

This paper enhances Monte Carlo methods for microcanonical calculations by applying a re-weighting technique, improving accuracy in systems with phase transitions, exemplified by the four-state Potts model.

Contribution

It introduces a re-weighting approach to extend canonical Monte Carlo algorithms, enabling more precise microcanonical analysis of phase transitions.

Findings

Detected small latent heat in the four-state Potts model.

Observed power-law size dependence of latent heat with exponent ~0.26.

Discussed the implications for the nature of phase transitions as system size grows.

Abstract

Velazquez and Curilef have proposed a methodology to extend Monte Carlo algorithms that are based on canonical ensemble. According to our previous study, their proposal allows us to overcome slow sampling problems in systems that undergo any type of temperature-driven phase transition. After a comprehensive review about ideas and connections of this framework, we discuss the application a re-weighting technique to improve the accuracy of microcanonical calculations, specifically, the well-known multi-histograms method of Ferrenberg and Swendsen. As example of application, we reconsider the study of four-state Potts model on the square lattice $L\times L$ with periodic boundary conditions. This analysis allows us to detect the existence of a very small latent heat per site $q_{L}$ during the occurrence of temperature-driven phase transition of this model, whose size dependence seems to follow a power-law $q_{L}(L)\propto(1/L)^{z}$ with exponent $z\simeq0$.$26\pm0$.$02$. It is discussed the compatibility of these results with the continuous character of temperature-driven phase transition when $L\rightarrow+\infty$.