The three-colour model with domain wall boundary conditions

Details The three-colour model with domain wall boundary conditions The three-colour model with domain wall boundary conditions

2009-11-03

arxiv.org/abs/0911.0561v2

Adv. Appl. Math 46 (2011), 481-535

Mathematics

Combinatorics

Version 2: Minor changes, references added.

Scientific paper

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.

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