Calculation of the Residual Entropy of Ice Ih by Monte Carlo simulation with the Combination of the Replica-Exchange Wang-Landau algorithm and Multicanonical Replica-Exchange Method

TL;DR

This paper presents a novel Monte Carlo simulation approach combining Replica-Exchange Wang-Landau and Multicanonical methods to accurately estimate the residual entropy of ice Ih, achieving results with very high precision.

Contribution

The study introduces a new simulation protocol that improves the accuracy of residual entropy estimation for ice Ih using advanced Monte Carlo techniques.

Findings

Residual entropy estimate within 0.038% of series expansion

Estimate within 0.000077% of PEPS algorithm

Highlights importance of random number generator uniformity

Abstract

We estimated the residual entropy of ice Ih by the recently developed simulation protocol, namely, the combination of Replica-Exchange Wang-Landau algorithm and Multicanonical Replica-Exchange Method. We employed a model with the nearest neighbor interactions on the three-dimensional hexagonal lattice, which satisfied the ice rules in the ground state. The results showed that our estimate of the residual entropy is found to be within 0.038 % of series expansion estimate by Nagle and within 0.000077 % of PEPS algorithm by Vanderstraeten. In this article, we not only give our latest estimate of the residual entropy of ice Ih but also discuss the importance of the uniformity of a random number generator in MC simulations.