Phase coexistence and torpid mixing in the 3-coloring model on Z^d

SIAM Journal on Discrete Mathematics, 2012.

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Abstract:

We show that for all sufficiently large d, the uniform proper 3-coloring model (in physics called the 3-state antiferromagnetic Potts model at zero temperature) on Z^d admits multiple maximal-entropy Gibbs measures. This is a consequence of the following combinatorial result: if a proper 3-coloring is chosen uniformly from a box in Z^d,...More

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