A Rapidity-Independent Parameter in the Star-Triangle Relation

Abstract

The normalization factor in the star-triangle relation can be evaluated in a simple form by taking determinants. If we combine this with the rotation symmetries, then we can show that a certain simple quantity I has to be independent of the rapidities. In this sense it is an invariant. We evaluate it for several particular models and find it is one for self-dual models, and is related to the modulus k (or k ′) for the Ising, Kashiwara-Miwa and chiral Potts models.