Computer simulation of two continuous spin models using Wang-Landau-Transition-Matrix Monte Carlo Algorithm

TL;DR

This paper evaluates a combined Wang-Landau and Transition Matrix Monte Carlo algorithm for simulating continuous spin models, demonstrating its effectiveness on the Lebwohl-Lasher and XY models.

Contribution

It introduces and tests a hybrid Monte Carlo algorithm for continuous energy lattice spin models, providing insights into its performance and optimization.

Findings

The WLTM algorithm accurately reproduces known solutions for the Lebwohl-Lasher model.

The algorithm effectively simulates the two-dimensional XY model.

Recommendations for optimizing the algorithm's performance in continuous systems.

Abstract

Monte Carlo simulation using a combination of Wang Landau (WL) and Transition Matrix (TM) Monte Carlo algorithms to simulate two lattice spin models with continuous energy is described. One of the models, the one dimensional Lebwohl-Lasher model has an exact solution and we have used this to test the performance of the mixed algorithm (WLTM). The other system we have worked on is the two dimensional XY-model. The purpose of the present work is to test the performance of the WLTM algorithm in continuous models and to suggest methods for obtaining best results in such systems using this algorithm.