Phase transitions in centered-rectangular- and square-lattice-gas models

Phase transitions in centered-rectangular- and square-lattice-gas models have been studied by transfer-matrix methods, with the use of finite-size scaling ideas. The transition lines and critical exponents have been obtained for the $p(2\mathrm{}\times 1)$ and $p(2\mathrm{}\times 2)$ structures for the centered-rectangular model with several pairwise interactions and a three-body interaction. This model is of interest in that the $p(2\mathrm{}\times 1)$ and $p(2\mathrm{}\times 2)$ transitions belong to the universality class of the $\mathrm{XY}$ model with cubic anisotropy and hence the critical exponents are nonuniversal. As well, it is a simple model of O on W(110). The transition lines have also been obtained for a square-lattice-gas model with competing interactions, for the (2×1) and (2×2) ordered structures. The importance of finite-size effects is demonstrated for both models.