New series of 3D lattice integrable models

TL;DR

This paper introduces a new series of 3D integrable lattice models with N colors, generalizing previous elliptic models, featuring modified tetrahedron equations, elliptic parameterization, and two free parameters.

Contribution

It presents a novel family of 3D lattice models with N colors, extending prior elliptic models, and satisfying modified tetrahedron equations with new parameterization.

Findings

Models satisfy modified tetrahedron equations.

Weights are parameterized by elliptic functions.

Models include two free parameters: elliptic modulus and η.

Abstract

In this paper we present a new series of 3-dimensional integrable lattice models with $N$ colors. The case $N=2$ generalizes the elliptic model of our previous paper. The weight functions of the models satisfy modified tetrahedron equations with $N$ states and give a commuting family of two-layer transfer-matrices. The dependence on the spectral parameters corresponds to the static limit of the modified tetrahedron equations and weights are parameterized in terms of elliptic functions. The models contain two free parameters: elliptic modulus and additional parameter $\eta$. Also we briefly discuss symmetry properties of weight functions of the models.