The vertex formulation of the Bazhanov-Baxter Model

TL;DR

This paper introduces a new integrable vertex model on a cubic lattice with N-valued spins, satisfying the Tetrahedron Equation, and connects it to the Bazhanov-Baxter Model, reproducing known solutions for N=2.

Contribution

It formulates a vertex model on a cubic lattice with N-valued spins that obeys the Tetrahedron Equation, extending the integrable models framework.

Findings

Model is equivalent to Bazhanov-Baxter Model in the thermodynamic limit.

Reproduces Korepanov's and Hietarinta's solutions for N=2.

Provides a new vertex formulation for the integrable model.

Abstract

In this paper we formulate an integrable model on the simple cubic lattice. The $N$ -- valued spin variables of the model belong to edges of the lattice. The Boltzmann weights of the model obey the vertex type Tetrahedron Equation. In the thermodynamic limit our model is equivalent to the Bazhanov -- Baxter Model. In the case when $N=2$ we reproduce the Korepanov's and Hietarinta's solutions of the Tetrahedron equation as some special cases.