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
Author
Hjalmar Rosengren
Chalmers, Mathematical Sciences, Mathematics
University of Gothenburg
Advances in Applied Mathematics
0196-8858 (ISSN) 1090-2074 (eISSN)
Vol. 46 1-4 481-535Subject Categories
Mathematics
Roots
Basic sciences
DOI
10.1016/j.aam.2010.10.007