The Eight Vertex Model.New results

TL;DR

This paper advances understanding of the eight-vertex model by constructing eigenvectors for degenerate eigenvalues and exploring the hidden elliptic symmetry, complementing existing eigenvalue tools.

Contribution

It introduces a method to construct eigenvectors for degenerate eigenvalues and discusses the associated hidden elliptic symmetry, filling gaps in the model's spectral analysis.

Findings

Eigenvectors for degenerate eigenvalues are explicitly constructed.

The hidden elliptic symmetry of the model is analyzed.

The work enhances the spectral understanding of the eight-vertex model.

Abstract

Whereas the tools to determine the eigenvalues of the eight-vertex transfer matrix T are well known there has been until recently incomplete knowledge about the eigenvectors of T. We describe the construction of eigenvectors of T corresponding to degenerate eigenvalues and discuss the related hidden elliptic symmetry.