Three-coloring statistical model with domain wall boundary conditions. II. Trigonometric limit

TL;DR

This paper explores a specific trigonometric limit of the three-coloring statistical model with domain wall boundary conditions, solving functional equations and deriving a new determinant formula for partial partition functions.

Contribution

It introduces a novel trigonometric limit analysis, solving functional equations and providing a determinant representation for the model's partial partition functions.

Findings

Functional equations are explicitly solved in the trigonometric limit.

A new determinant formula for partial partition functions is derived.

The results enhance understanding of the model's mathematical structure.

Abstract

A nontrivial trigonometric limit of the three-coloring statistical model with the domain wall boundary conditions is considered. In this limit the functional equations, constructed in the previous paper, are solved and a new determinant representation for the partial partition functions is found.