Improving the efficiency of Monte Carlo simulations of systems that undergo temperature-driven phase transitions

TL;DR

This paper demonstrates that a recently proposed Monte Carlo extension improves simulation efficiency near critical points and phase transitions, outperforming traditional algorithms in the 2D four-state Potts model.

Contribution

It shows that the extended Monte Carlo methodology enhances efficiency near critical points, surpassing standard cluster algorithms in specific phase transition simulations.

Findings

Extended Metropolis outperforms Swendsen-Wang and Wolff algorithms.

Methodology is effective for various temperature-driven phase transitions.

Significant efficiency gains near critical points observed.

Abstract

Recently, Velazquez and Curilef have proposed a methodology to extend Monte Carlo algorithms based on canonical ensemble, which is aimed to overcome slow sampling problems associated with temperature-driven discontinuous phase transitions. We show in this work that Monte Carlo algorithms extended with this methodology also exhibit a remarkable efficiency near a critical point. Our study is performed for the particular case of 2D four-state Potts model on the square lattice with periodic boundary conditions. This analysis reveals that the extended version of Metropolis importance sample is more efficient than the usual Swendsen-Wang and Wolff cluster algorithms. These results demonstrate the effectiveness of this methodology to improve the efficiency of MC simulations of systems that undergo any type of temperature-driven phase transition.