Soft-Sphere Equation of State

The pressure and entropy for soft-sphere particles interacting with an inverse twelfth-power potential are determined using the Monte Carlo method. The solid-phase entropy is calculated in two ways: by integrating the single-occupancy equation of state from the low density limit to solid densities, and by using solid-phase Monte Carlo pressures to evaluate the anharmonic corrections to the lattice-dynamics high-density limit. The two methods agree, and the entropy is used to locate the melting transition. The computed results are compared with the predictions of the virial series, lattice dynamics, perturbation theories, and cell models. For the fluid phase, perturbation theory is very accurate up to two-thirds of the freezing density. For the solid phase, a correlated cell model predicts pressures very close to the Monte Carlo results.