Spatial updating in the great grand canonical ensemble

Abstract

In spatial updating grand canonical Monte Carlo, particle transfers are implemented by examining the local environment around a point in space. In the present work, these algorithms are extended to very high densities by allowing the volume to fluctuate, thus forming a great grand canonical ensemble. Since fluctuations are unbounded, a constraint must be imposed. The constrained ensemble may be viewed as a superposition of either constant-pressure or grand canonical ensembles. Each simulation of the constrained ensemble requires a set of weights that must be determined iteratively. The outcome of a single simulation is the density of states in terms of all its independent variables. Since all extensive variables fluctuate, it is also possible to estimate absolute free energies and entropies from a single simulation. The method is tested on a system of hard spheres and the transition from the fluid to a face-centered cubic crystal is located with high precision.