Elliptic gamma-function and multi-spin solutions of the Yang-Baxter equation

TL;DR

This paper generalizes the quantum Yang-Baxter equation solution to multi-component continuous spins using elliptic gamma-functions, leading to new integrable models and classical equations.

Contribution

It introduces a multi-spin extension of the Yang-Baxter solution with elliptic gamma-function weights, expanding the scope of integrable lattice models.

Findings

Derived a multi-component spin model with elliptic gamma-function weights

Established equivalences with interaction-round-a-face models

Connected the quantum model to new classical integrable equations

Abstract

We present a generalization of the master solution to the quantum Yang-Baxter equation (obtained recently in arXiv:1006.0651) to the case of multi-component continuous spin variables taking values on a circle. The Boltzmann weights are expressed in terms of the elliptic gamma-function. The associated solvable lattice model admits various equivalent descriptions, including an interaction-round-a-face formulation with positive Boltzmann weights. In the quasi-classical limit the model leads to a new series of classical discrete integrable equations on planar graphs.