Residual entropy of ice Ih by Wang–Landau Monte Carlo simulation of an effective Ising model

Abstract

Abstract Accurate evaluation of the residual entropy of three-dimensional ice systems remains a difficult task. In this work, we estimate the residual entropy of ice Ih (ordinary ice) by an improvement of the Wang–Landau Monte Carlo algorithm, which directly calculates the density of states of the system. We define an effective three-dimensional Ising model with nearest-neighbour interactions, and introduce the mapping of the spin configurations of this Ising model into the hydrogen configurations of ice Ih. The ground states of this Ising model are equivalent with the hydrogen configurations obeying the ice rules, therefore the ground state degeneracy directly determines the residual entropy. Our estimate is in good agreement with the famous theoretical approximation by Nagle in 1966, and other results evaluated from various methods. The advantage of making use of the equivalent Ising model is discussed. It is convenient to extend our approach to other lattice systems.