Ising Model for the Freezing Transition

A spin-1 Ising model incorporating positional order to a standard lattice gas with no attractive interactions is introduced and found to be consistent with all known attributes of the freezing transition of the hard-sphere system. Implementation of attractive interactions in a fairly natural way then allows every aspect of the phase diagram of a simple substance to be reproduced. The \emph{whole} phase behavior of such sort of substances is thus found to sharply manifest the van der Waals picture highlighting the relevance of harsh repulsive forces.