Baxter-Bazhanov Model, Frenkel-Moore Equation and the Braid Group

TL;DR

This paper explores the duality of a 3D vertex model related to the Baxter-Bazhanov model, constructs the associated braid group, and presents a related deformed vertex model with implications for 3D lattice integrability.

Contribution

It introduces a dual 3D vertex model, constructs the braid group for the Frenkel-Moore equation, and presents a deformed vertex model related to existing 3D integrable models.

Findings

Constructed the braid group for the Frenkel-Moore equation.

Identified transformations acting as braid rotations.

Presented a deformed vertex model related to existing 3D lattice models.

Abstract

In this paper the three-dimensional vertex model is given, which is the duality of the three-dimensional Baxter-Bazhanov (BB) model. The braid group corresponding to Frenkel-Moore equation is constructed and the transformations $R, I$ are found. These maps act on the group and denote the rotations of the braids through the angles $\pi$ about some special axes. The weight function of another three-dimensional vertex model related the 3D lattice integrable model proposed by Boos, Mangazeev, Sergeev and Stroganov is presented also, which can be interpreted as the deformation of the vertex model corresponding to the BB model.