An Iterative Solution of the Three-colour Problem on a Random Lattice

TL;DR

This paper extends Baxter's three-colour problem to random lattices, analyzing its critical behavior through matrix models and developing a recursive algorithm for solutions.

Contribution

It introduces a novel recursive algorithm for solving the three-colour problem on random lattices using matrix model reformulation.

Findings

Analysis of the analyticity structure of the matrix model

Identification of critical behavior in the model

Development of a recursive solution algorithm

Abstract

We study the generalisation of Baxter's three-colour problem to a random lattice. Rephrasing the problem as a matrix model problem we discuss the analyticity structure and the critical behaviour of the resulting matrix model. Based on a set of loop equations we develop an algorithm which enables us to solve the three-colour problem recursively