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

2013/07/29 by L. Velázquez, L. Velazquez, Juan Carlos Castro-Palacio +1 · 6 citations
Materials Science · Mathematics · Physics and Astronomy · #Boundary value problem #Computer science #Dynamic Monte Carlo method #Hybrid Monte Carlo #Ising model #Markov chain Monte Carlo #Material Dynamics and Properties #Mathematical analysis #Mathematics #Monte Carlo method #Monte Carlo method in statistical physics #Monte Carlo molecular modeling #Periodic boundary conditions #Phase transition #Physics #Potts model #Sampling (signal processing) #Square lattice #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Thermodynamics #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.88.013311

published in Physical Review E 88(1), 013311 (American Physical Society) · Version accepted for publicacion in Physical Review E

arxiv created 2013/07/29 · openalex publication_date 2013/07/29 · arxiv updated 2013/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Recently, Velazquez and Curilef proposed a methodology to extend Monte Carlo algorithms based on a canonical ensemble which aims 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 a two-dimensional four-state Potts model on a square lattice with periodic boundary conditions. This analysis reveals that the extended version of Metropolis importance sampling 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.

Citations

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