A Lattice Model of a Classical Hard Sphere Gas: II

It was shown in a previous publication that the antiferromagnetic Ising model could be transformed into a model of a hard sphere lattice gas. It was seen that, for the model on the loose packed lattices, a transition from an ordered to a disordered phase was suggested. No firm results could be obtained, however, since the approximation used for the ordered phase was inadequate. It is now shown that the pressure and free energy curves of both phases can be calculated on the Bethe and `ring' approximations. In each case a transition is shown to occur and to be of the second order.