Exact solvability of an Ising-type model, and exact solvability of the 6-vertex, and 8-vertex, models

TL;DR

This paper demonstrates the exact solvability of an Ising-type model and its relation to the 6-vertex and 8-vertex models, providing new insights into integrability and algebraic structures in statistical mechanics.

Contribution

It introduces a method to establish the exact solvability of an Ising-type model that interpolates between the 6-vertex and 8-vertex models, expanding understanding of integrable systems.

Findings

Computed action-angle coordinates for the Ising-type model.

Identified dependencies on nearest neighbor interactions in Poisson brackets.

Established the exact solvability of a model interpolating between 6-vertex and 8-vertex models.

Abstract

We compute the action-angle coordinates for an Ising type model whose L-operator has been previously studied in the literature by Bazhanov and Sergeev. In comparison to computations with such operators that have been examined previously by the author for the 4-vertex, 6-vertex, and 20-vertex, models, computations for asymptotically approximating a collection of sixteen identities with the Poisson bracket, which together constitute the Poisson structure of the Ising type model, exhibit dependencies upon nearest neighbor interactions. Inspite of the fact that L-operators for the 20-vertex model are defined in terms of combinatorial, and algebraic, constituents unlike such operators for the 6-vertex model which are defined in terms of projectors and Pauli basis elements, L-operators for the Ising-type model can be used for concluding that a model which interpolates between the 6-vertex, and 8-vertex, models is exactly solvable.