SOLUTIONS OF THE STAR-TRIANGLE EQUATIONS IN (N_α,N_β) POTTS MODELS

In this paper we present the solutions of the star-triangle equation for Boltzmann weights of the (N_α,N_β) model. This model consists of two scalar Potts models (of N_α and N_β states, respectively) coupled together by four-spin interaction terms and was introduced by Domany and Riedel to study the phase transitions in adsorbed thin films. If N_α,N_β≠2, the star-triangle equations have nontrivial self-dual and non-self-dual solutions only for N_α=N_β; whereas if N_α≠N_β=2, we have other self-dual and non-self-dual solutions. After applying partial duality transformations several of our solutions can be identified with known solutions for Interaction-Round-a-Face (IRF) models. Our results also mean that our high-genus solutions found earlier are not the only solutions to the star-triangle equations in chiral Potts models with six or more states per site.