Three-coloring statistical model with domain wall boundary conditions. I. Functional equations

Details Three-coloring statistical model with domain wall boundary conditions. I. Functional equations Three-coloring statistical model with domain wall boundary conditions. I. Functional equations

2008-05-06

arxiv.org/abs/0805.0669v2

Physics

Mathematical Physics

16 pages, notations changed for consistency with the next part, appendix added

Scientific paper

In 1970 Baxter considered the statistical three-coloring lattice model for the case of toroidal boundary conditions. He used the Bethe ansatz and found the partition function of the model in the thermodynamic limit. We consider the same model but use other boundary conditions for which one can prove that the partition function satisfies some functional equations similar to the functional equations satisfied by the partition function of the six-vertex model for a special value of the crossing parameter.

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