A Monte Carlo study of the freezing transition of hard spheres

A simulation method for fluid-solid transitions, which is based on a modification of the constrained cell model of Hoover and Ree, is developed and tested on a system of hard spheres. In the fully occupied constrained cell model, each particle is confined in its own Wigner-Seitz cell. Constant-pressure simulations of the constrained cell model for a system of hard spheres indicate a point of mechanical instability at a density which is about 64% of the density at the close packed limit. Below that point, the solid is mechanically unstable since without the confinement imposed by the cell walls it will disintegrate to a disordered, fluid-like phase. Hoover and Ree proposed a modified cell model by introducing an external field of variable strength. High values of the external field variable favor configurations with one particle per cell and thus stabilize the solid phase. In this work, the modified cell model of a hard-sphere system is simulated under constant-pressure conditions using tempering and histogram reweighting techniques. The simulations indicate that as the strength of the field is reduced, the transition from the solid to the fluid phase is continuous below the mechanical instability point and discontinuous above. The fluid-solid transition of the hard-sphere system is determined by analyzing the field-induced fluid-solid transition of the modified cell model in the limit in which the external field vanishes. The coexistence pressure and densities are obtained through finite-size scaling techniques and are in good accord with previous estimates.