The six and eight-vertex models revisited

TL;DR

This paper revisits the six and eight-vertex models in statistical mechanics, clarifying the transfer matrix equations and revealing connections between various solvable models to deepen understanding of their structure.

Contribution

It presents a clearer formulation of the transfer matrix equations for these models, highlighting their relationships with other integrable models and offering new insights into their structure.

Findings

Explicit and transparent notation for transfer matrix equations

Revealed relationships between six-vertex, eight-vertex, and other models

Enhanced understanding of solvable models in statistical mechanics

Abstract

Elliott Lieb's ice-type models opened up the whole field of solvable models in statistical mechanics. Here we discuss the ``commuting transfer matrix'' $T, Q$ equations for these models, writing them in a more explicit and transparent notation that we believe offers new insights. The approach manifests the relationship between the six-vertex and chiral Potts models, and between the eight-vertex and Kashiwara-Miwa models.