Phase coexistence in partially symmetric q-state models

The authors consider a lattice model whose spins may assume a finite number q of values. The interaction energy between two nearest-neighbor spins takes on the value J1+J2 or J2, depending on whether the two spins coincide or are different but coincide modulo q1, and it is zero otherwise. This model is a generalization of the Ashkin-Teller model and exhibits the multilayer wetting phenomenon, that is, wetting by one or two or three interfacial layers, depending on the number of phases in coexistence. While the authors plan to consider interface properties in such a case, here they study the phase diagram of the model. It is shown that for large values of q1 and q/q1, it exhibits, according the value of J2/J1, either a unique first-order temperature-driven phase transition at some point βt where q ordered phases coexist with the disordered one, or two transition temperatures βt(1) and βt(2), where q1 partially ordered phases coexist with the ordered ones (βt(1)) or with the disordered one (βt(2)), or for a particular value J2/J1 there is a unique transition temperature where all the previous phases coexist. Proofs are based on the Pirogov-Sinai theory: the authors perform a random cluster representation of the model allowing us to consider noninteger values of q1 and q/q1 to which they adapt this theory. 20 refs., 2 figs