Mean-field fluid behavior of the Gaussian core model

We show that the Gaussian con model of particles interacting via a penetrable repulsive Gaussian potential, first considered by Stillinger [J. Chem. Phys. 65, 3968 (1976)], behaves as a weakly correlated "mean-field fluid" over a surprisingly wide density and temperature range. In the bulk, the structure of the fluid phase is accurately described by the random phase approximation for the direct correlation function, and by the more sophisticated hypernetted chain integral equation. The resulting pressure deviates very little from a simple mean-field-like quadratic form in the density, while the low density virial expansion turns out to have an extremely small radius of convergence. Density profiles near a hard wall are also very accurately described by the corresponding mean-field free-energy functional. The binary version of the model exhibits a spinodal instability against demixing at high densities. Possible implications for semidilute polymer solutions are discussed.