Fluid and solid phases of the Gaussian core model

We study the structural and thermodynamic properties of a model of point particles interacting by means of a Gaussian pair potential first introduced by Stillinger (Stillinger F H 1976 J. Chem. Phys. 65 3968). By employing integral equation theories for the fluid state and comparing with Monte Carlo simulation results, we establish the limits of applicability of various common closures and examine the dependence of the correlation functions of the liquid on the density and temperature. We employ a simple, mean-field theory for the high-density domain of the liquid and demonstrate that at infinite density the mean-field theory is exact and that the system reduces to an 'infinite-density ideal gas', where all correlations vanish and where the hypernetted-chain (HNC) closure becomes exact. By employing an Einstein model for the solid phases, we subsequently calculate quantitatively the phase diagram of the model and find that the system possesses two solid phases, face-centred cubic and body-centred cubic, and also displays re-entrant melting into a liquid at high densities. Moreover, the system remains fluid at all densities when the temperature exceeds 1% of the strength of the interactions.