Magnetic hard squares: exact solution

A three-state IRF model of a magnetic hard-square lattice gas with anisotropic interactions is solved exactly on special two-dimensional manifolds in the full five-dimensional thermodynamic space spanned by the (ferro- or antiferro-) magnetic interactions J, K, the (attractive or repulsive) lattice-gas interactions L, M and the activity z. The phase boundaries determined include multicritical lines and critical surfaces as well as first-order surfaces of three- and fivefold phase coexistence between the fluid and various (para, ferro, etc.) magnetic square-ordered solid phases. Analytic expressions are given for free energies, interfacial tensions, correlation lengths, sublattice densities and magnetisations. The critical behaviour of these quantities is studied and the associated critical exponents obtained.