Optimising the parameters of the Gibbs Ensemble Monte Carlo simulation of phase separation: the role of multiple relaxation times

Abstract

ABSTRACTWe address the problem of how to choose the parameters of a Gibbs Ensemble Monte Carlo (GEMC) simulation of phase separation optimally through a systematic study of the autocorrelation functions of density fluctuation in a particular example. In this model the particles interact via a square well potential. Values of the temperature as well as the range of the square well potential are varied. We find that the normalised autocorrelation function is described accurately over a very large time scale as a linear combination of an exponential function with a time scale τ2 and a stretched exponential function with a time scale τ1 and an exponent α. Dependence of α, τ1 and τ2 on the temperature, the parameters of the GEMC algorithm and the range of the square well potential is investigated and interpreted. We use the insight thus obtained and the generality of some aspects of these results to construct the route to optimisation of the parameters of a GEMC simulation in a somewhat more generic situation involving a single-component phase separation.