MULTICANONICAL MONTE-CARLO STUDY OF SOLID-SOLID PHASE COEXISTENCE IN A MODEL COLLOID

We describe a Monte Carlo approach to the determination of the relativ e stability of two phases, which is conceptually direct, potentially r ather 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 distinguis hing the two phases. The transition frequencies are observed in simula tions initiated from macrostates with order-parameter values intermedi ate between those of the two phases; they are used to provide estimato rs of the macrostate transition probability matrix and thence estimato rs of the sampling distribution itself. The procedure allows one to co nstruct a series of sampling distributions, weighted with respect to t he canonical distribution, which approach the multicanonical limit, fl at across order-parameter space. It entails only simulations that are short compared to the (multicanonical) relaxation time of the order pa rameter. Reweighting the transition-probability estimator of the multi canonical sampling distribution provides a good estimate of the canoni cal distribution of the order parameter for any value of the conjugate field, permitting the identification of the coexistence field in part icular. The method is developed in the context of a system of hard sph eres with short-range attractive interactions, described by a square p otential well, which provides a simple model of the intercolloid deple tion potential in colloid-polymer mixtures. In particular we explore t he phase diagram in the region in which studies by others, based on fr ee energy evaluation by thermodynamic integration, have shown the coex istence of two fee solid phases of different densities.