Baxter has solved a restricted class of square lattice gas models with nearest-neighbor exclusion (thus "hard squares") and next-nearest-neighbor interactions. Arguments are presented which demonstrate that the subspace spanned by his exact solution contains the line of tricritical points and the associated surface of first-order transitions of hard squares with attractive next-nearest-neighbor interactions. The tricritical exponents so identified confirm those obtained by Nienhuis for a dilute Ising model.
Abstract Two infinite range Ising models are solved exactly using a microcanonical ensemble in the longrange order parameter. Classical tricritical points exist for both models. The first model involving two‐spin and four‐spin terms is relevant to the compressible Ising model. The other model is the infinite range version of the Blume‐Capel spin‐one Ising model. In both the cases the exact free‐energy functions calculated are examples of exact classical Landau free‐energy functions with tricritical point behaviour.