Generalized $XYZ$ Model Associated to Sklyanin Algebra$^*$

TL;DR

This paper extends the Heisenberg XYZ model to higher spin representations using the Sklyanin algebra, calculating its free energy via a generalized Bethe Ansatz, contributing to integrable systems in mathematical physics.

Contribution

It introduces a generalized XYZ model associated with the Sklyanin algebra and computes its free energy using an advanced Bethe Ansatz method.

Findings

Explicit free energy expression for the generalized model

Extension of Bethe Ansatz techniques to higher spin representations

Connection between Sklyanin algebra and integrable lattice models

Abstract

The free energy of a lattice model, which is a generalization of the Heisenberg $XYZ$ model with the higher spin representation of the Sklyanin algebra, is calculated by the generalized Bethe Ansatz of Takhtajan and Faddeev. (Talk given at the XXI Differential Geometry Methods in Theoretical Physics, Tianjin, China 5-9 June 1992)