Multicanonical Monte Carlo study of solid-solid phase coexistence in a model colloid

We describe a Monte Carlo approach to the determination of the relative stability of two phases, which is conceptually direct, potentially rather general, and particularly well suited to parallel computers. The approach exploits the information contained in the frequencies of the transitions between the macrostates of the order parameter distinguishing the two phases. The transition frequencies are observed in simulations initiated from macrostates with order-parameter values intermediate between those of the two phases; they are used to provide estimators of the macrostate transition probability matrix and thence estimators of the sampling distribution itself. The procedure allows one to construct a series of sampling distributions, weighted with respect to the canonical distribution, which approach the multicanonical limit, flat across order-parameter space. It entails only simulations that are short compared to the (multicanonical) relaxation time of the order parameter. Reweighting the transition-probability estimator of the multicanonical sampling distribution provides a good estimate of the canonical distribution of the order parameter for any value of the conjugate field, permitting the identification of the coexistence field in particular. The method is developed in the context of a system of hard spheres with short-range attractive interactions, described by a square potential well, which provides a simple model of the intercolloid depletion potential in colloid-polymer mixtures. In particular we explore the phase diagram in the region in which studies by others, based on free energy evaluation by thermodynamic integration, have shown the coexistence of two fee solid phases of different densities.