On the Three-dimensional Lattice Model

TL;DR

This paper demonstrates that a specific three-dimensional lattice spin model with N states, proposed by Mangazeev, Sergeev, and Stroganov, is a special case of the well-known Bazhanov-Baxter model using the restricted star-triangle relation.

Contribution

It establishes the integrability of the model by relating it to the Bazhanov-Baxter model through the restricted star-triangle relation.

Findings

The model is a particular case of the Bazhanov-Baxter model.

The restricted star-triangle relation is used to prove integrability.

The model's structure is clarified within the integrable systems framework.

Abstract

Using the restricted star-triangle relation, it is shown that the $N$-state spin integrable model on a three-dimensional lattice with spins interacting round each elementary cube of the lattice proposed by Mangazeev, Sergeev and Stroganov is a particular case of the Bazhanov-Baxter model.