Functional Equations and Fusion Matrices for the Eight Vertex Model

TL;DR

This paper derives functional equations for the eight vertex model, revealing special reductions of fusion matrices at roots of unity and comparing these findings with Sklyanin's algebra.

Contribution

It introduces a novel set of functional equations for the eight vertex model and identifies specific reductions of fusion matrices at roots of unity.

Findings

Fusion matrices reduce at roots of unity for orders 3, 4, and 5.

The functional equations are analogous to those of the chiral Potts model.

Comparison with Sklyanin's algebra highlights structural similarities.

Abstract

We derive sets of functional equations for the eight vertex model by exploiting an analogy with the functional equations of the chiral Potts model. From these equations we show that the fusion matrices have special reductions at certain roots of unity. We explicitly exhibit these reductions for the 3,4 and 5 order fusion matrices and compare our formulation with the algebra of Sklyanin.