Two-dimensional lattice gas models with extremely anisotropic spin interactions

The effect of anisotropic magnetic interactions on the physical properties of lattice gases is considered in the framework of two simple models, consisting of particles that carry an n-component classical spin (unit vector, n=2 or 3), and associated with a two-dimensional square lattice; each site can host one particle at most, thus implicitly allowing for hard-core repulsion; the pair potential, restricted to nearest neighbors, is ferromagnetic and extremely anisotropic in spin space, in the sense that only one component is involved in the interaction; the models are rigorously known to support an orientational ordering transition in appropriate ranges of temperature and chemical potential. Thermodynamic properties and phase diagrams of both models have been studied by means of mean-field and two-site cluster treatments, and their tricritical points have been identified. The case of zero chemical potential has been investigated by Monte Carlo simulations, so as to obtain a quantitative test of the named approximations, as well as a more detailed physical characterization.