Wang-Landau Monte Carlo simulation of isotropic-nematic transition in liquid crystals

TL;DR

This paper investigates the Wang-Landau Monte Carlo method's effectiveness for simulating the isotropic-nematic transition in liquid crystals, proposing modifications to improve its performance on systems with continuous energy spectra.

Contribution

The paper introduces modifications to the Wang-Landau algorithm to better handle systems with continuous energy spectra, demonstrated on a liquid crystal model.

Findings

Original Wang-Landau algorithm performs poorly on continuous spectra

Modified algorithm shows improved performance on liquid crystal model

Successful simulation of isotropic-nematic transition using the modified method

Abstract

Wang and Landau proposed recently, a simple and flexible non-Boltzmann Monte Carlo method for estimating the density of states, from which the macroscopic properties of a closed system can be calculated. They demonstrated their algorithm by cocontinuous energy spectrum. We propose in this paper modifications nsidering systems with discrete energy spectrum. We find that the Wang-Landau algorithm does not perform well when the system has continuous energy spectrum. We propose in this paper modifications to the algorithm and demonstrate their performance on a lattice model of liquid crystalline system (with Lebwohl-Lasher interaction having continuously varying energy), exhibiting transition from high temperature isotropic to low temperature nematic phase.