The three-colour model with domain wall boundary conditions
Journal article, 2011

We study the partition function for the three-colour model with domain wall boundary conditions. We express it in terms of certain special polynomials, which can be constructed recursively. Our method generalizes Kuperberg's proof of the alternating sign matrix theorem, replacing the six-vertex model used by Kuperberg with the eight-vertex-solid-on-solid model. As applications, we obtain some combinatorial results on three-colourings. We also conjecture an explicit formula for the free energy of the model. (C) 2010 Elsevier Inc. All rights reserved.

8-vertex model

Alternating sign matrix

Partition function

6-vertex model

Eight-vertex-solid-on-solid model

affine root system

Three-colour model

Domain wall boundary conditions


Hjalmar Rosengren

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Advances in Applied Mathematics

0196-8858 (ISSN) 1090-2074 (eISSN)

Vol. 46 1-4 481-535

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