Quasi-classical expansion of a hyperbolic solution to the star-star relation and multicomponent 5-point difference equations

TL;DR

This paper explores the quasi-classical limit of a multicomponent hyperbolic spin solution related to the star-star relation, leading to new multicomponent 5-point difference equations extending scalar cases.

Contribution

It introduces n-1-component extensions of scalar 5-point equations derived from the quasi-classical limit of hyperbolic solutions, advancing integrability and consistency studies.

Findings

Derived multicomponent 5-point difference equations

Extended scalar equations to multicomponent versions

Linked equations to integrability on face-centered cubics

Abstract

The quasi-classical expansion of a multicomponent spin solution of the star-star relation with hyperbolic Boltzmann weights is investigated. The equations obtained in a quasi-classical limit provide n-1-component extensions of certain scalar 5-point equations (corresponding to n=2) that were previously investigated by the author in the context of integrability and consistency of equations on face-centered cubics.