The three-colour model with domain wall boundary conditions
Artikel i vetenskaplig tidskrift, 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

Författare

Hjalmar Rosengren

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Advances in Applied Mathematics

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

Vol. 46 1-4 481-535

Ämneskategorier

Matematik

Fundament

Grundläggande vetenskaper

DOI

10.1016/j.aam.2010.10.007