An Iterative Solution of the Three-colour Problem on a Random Lattice
arXiv:cond-mat/9710199 · doi:10.1016/S0550-3213(98)00042-X
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
14 pages, LaTeX, misprints corrected, approximation of (6.20) refined
References in corpus (1)
Cited by in corpus (20)
- D-particles, Matrix Integrals and KP hierachy
- A recursive approach to the O(n) model on random maps via nested loops
- Relaxation in graph coloring and satisfiability problems
- The six-vertex model on random lattices
- Coloring Random Triangulations
- Rotational Symmetry Breaking in Multi-Matrix Models
- Geometrically constrained statistical systems on regular and random lattices: From folding to meanders
- Fully Packed O(n=1) Model on Random Eulerian Triangulations
- Exact Solution of the Three-color Problem on a Random Lattice
- Hamiltonian Cycles on a Random Three-coordinate Lattice
- Hamiltonian Cycles on Random Eulerian Triangulations
- Exact Meander Asymptotics: a Numerical Check
- A Renormalization Group Approach to A Yang-Mills Two Matrix Model
- Non-anomalous `Ward' identities to supplement large-N multi-matrix loop equations for correlations
- Noncommutative 3-colour scalar quantum field theory model in 2D
- Formal matrix integrals and combinatorics of maps
- On gonihedric loops and quantum gravity
- Phase transitions and random matrices
- Remarks on the eigenvalues distributions of D\leq 4 Yang-Mills matrix models
- Large-N Limit as a Classical Limit: Baryon in Two-Dimensional QCD and Multi-Matrix Models