SU(2) parameterisation of Baxter's model

Abstract

A parametrisation of the Boltzmann weights of Baxter's symmetric eight-vertex model (1982) is derived, using Cherednik's representation (1979) of the Zamolodchikov algebra, in terms of theta functions based on the weight lattice of SU(2). The Yang-Baxter equations are satisfied as a consequence of the associativity of the Zamolodchikov algebra. The derivation makes the connection of Baxter's model to the spin-1/2 representation of SU(2) explicit.