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 1-4 481-535Ämneskategorier
Matematik
Fundament
Grundläggande vetenskaper
DOI
10.1016/j.aam.2010.10.007