Exceptional solutions to the eight-vertex model and integrability of anisotropic extensions of massive fermionic models

TL;DR

This paper explores the integrability of anisotropic extensions of the Belavin model, linking exceptional solutions of the eight-vertex model to the factorization of the S-matrix, and relates these solutions to the XXZ and six-vertex models.

Contribution

It demonstrates integrability in massive anisotropic models through exceptional solutions of the eight-vertex model, establishing new connections with XXZ and six-vertex models.

Findings

Integrability holds for specific coupling constants in anisotropic massive models.

Exceptional solutions of the eight-vertex model are key to understanding S-matrix factorization.

Connections between the eight-vertex, XXZ, and six-vertex models are established.

Abstract

We consider several anisotropic extensions of the Belavin model, and show that integrability holds also for the massive case for some specific relations between the coupling constants. This is done by relating the S-matrix factorization property to the exceptional solutions of the eight-vertex model. The relation of exceptional solutions to the XXZ and six-vertex models is also shown.