Solution of the star-triangle equation in the S3 spin model

H. Moraal

R. J. Baxter, Jacques H. H. Perk, Helen Au-Yang

V. V. Bazhanov, R. J. Baxter

Theodore W. Burkhardt, Ihnsouk Guim

Helen Au-Yang, Jacques H. H. Perk

In this paper we present the solutions of the star-triangle equation for Boltzmann weights of the (Nα,Nβ) model. This model consists of two scalar Potts models (of Nα and Nβ 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 Nα,Nβ≠2, the star-triangle equations have nontrivial self-dual and non-self-dual solutions only for Nα=Nβ; whereas if Nα≠Nβ=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.

Masao Nomura

Novel solutions to the star-triangle equation for the IRF model are presented which are described in terms of 6- j and 9- j symbols. Additivity of spectral parameters does not hold in this case.