Monte Carlo simulation of joint density of states of two continuous spin models using Wang-Landau-Transition-Matrix Algorithm

TL;DR

This paper applies Wang-Landau and Wang-Landau-Transition-Matrix Monte Carlo methods to compute the joint density of states in 1D Lebwohl-Lasher and 2D XY models, enabling detailed thermodynamic analysis.

Contribution

It introduces a combined Monte Carlo approach to accurately determine the joint density of states for continuous spin models.

Findings

Good agreement between the two algorithms' results.

Successful calculation of order parameter, susceptibility, and correlation functions.

Validation of the methods for continuous spin models.

Abstract

Monte Carlo simulation has been performed in one-dimensional Lebwohl-Lasher model and two dimensional XY-model using the Wang-Landau and the Wang-Landau-Transition-Matrix Monte Carlo methods. Random walk has been performed in the two-dimensional space comprising of energy-order parameter and energy-correlation function and the joint density of states (JDOS) were obtained. From the JDOS the order parameter, susceptibility and correlation function are calculated. Agreement between the results obtained from the two algorithms is very good.