Three-coloring statistical model with domain wall boundary conditions. I. Functional equations

TL;DR

This paper investigates a three-coloring lattice model with domain wall boundary conditions, deriving functional equations for its partition function, analogous to those of the six-vertex model, expanding understanding beyond toroidal boundaries.

Contribution

It introduces a new boundary condition analysis for the three-coloring model and establishes functional equations for its partition function, extending prior work on toroidal boundaries.

Findings

Partition function satisfies specific functional equations

Functional equations analogous to six-vertex model

Extension of boundary condition analysis

Abstract

In 1970 Baxter considered the statistical three-coloring lattice model for the case of toroidal boundary conditions. He used the Bethe ansatz and found the partition function of the model in the thermodynamic limit. We consider the same model but use other boundary conditions for which one can prove that the partition function satisfies some functional equations similar to the functional equations satisfied by the partition function of the six-vertex model for a special value of the crossing parameter.