Modified Tetrahedron Equations and Related 3D Integrable Models

TL;DR

This paper introduces a new class of 3D integrable models based on modified tetrahedron equations, utilizing elliptic functions for parameterization, and explores their mathematical properties and solutions.

Contribution

It presents a novel family of 3D integrable models derived from modified tetrahedron equations, with solutions expressed through elliptic functions and a free elliptic modulus parameter.

Findings

Construction of new 3D integrable models with commuting transfer-matrices

Parameterization of solutions using elliptic functions

Identification of models with a free elliptic modulus parameter

Abstract

Using a modified version of the tetrahedron equations we construct a new family of $N$-state three-dimensional integrable models with commuting two-layer transfer-matrices. We investigate a particular class of solutions to these equations and parameterize them in terms of elliptic functions. The corresponding models contain one free parameter $k$ -- an elliptic modulus.