Modified tetrahedron equation and related 3D integrable models,II

TL;DR

This paper provides analytical formulas for an N-state integrable spin model on a cubic lattice, enabling the construction of a family of commuting transfer matrices, simplifying the analysis of 3D integrable models.

Contribution

It introduces explicit analytical Boltzmann weights for a specific 3D integrable model, advancing beyond previous numerical solutions.

Findings

Analytical expressions for Boltzmann weights with elliptic dependence

Construction of a two-parametric family of commuting transfer matrices

Simplification of the model for further theoretical investigation

Abstract

This work is a continuation of paper (hep-th/9407146) where the Boltzmann weights for the N-state integrable spin model on the cubic lattice has been obtained only numerically. In this paper we present the analytical formulae for this model in a particular case. Here the Boltzmann weights depend on six free parameters including the elliptic modulus. The obtained solution allows to construct a two-parametric family of the commuting two-layer transfer matrices. Presented model is expected to be simpler for a further investigation in comparison with a more general model mentioned above.