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The three-colour model with domain wall boundary conditions

Hjalmar Rosengren (Institutionen för matematiska vetenskaper, matematik)
Advances in Applied Mathematics (0196-8858). Vol. 46 (2011), 1-4, p. 481-535.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Three-colour model, Eight-vertex-solid-on-solid model, Domain wall boundary conditions, Partition function, Alternating sign matrix, affine root system, 6-vertex model, 8-vertex model



Denna post skapades 2011-06-07. Senast ändrad 2014-09-29.
CPL Pubid: 141400

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematik

Chalmers infrastruktur