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

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

Comments: 14 pages, LaTeX, misprints corrected, approximation of (6.20) refined