Rapid Mixing for Lattice Colorings with Fewer Colors

Details Rapid Mixing for Lattice Colorings with Fewer Colors Rapid Mixing for Lattice Colorings with Fewer Colors

2005-08-30

arxiv.org/abs/cond-mat/0508737v1

Physics

Condensed Matter

Statistical Mechanics

Appeared in Proc. LATIN 2004, to appear in JSTAT

Scientific paper

We provide an optimally mixing Markov chain for 6-colorings of the square lattice on rectangular regions with free, fixed, or toroidal boundary conditions. This implies that the uniform distribution on the set of such colorings has strong spatial mixing, so that the 6-state Potts antiferromagnet has a finite correlation length and a unique Gibbs measure at zero temperature. Four and five are now the only remaining values of q for which it is not known whether there exists a rapidly mixing Markov chain for q-colorings of the square lattice.

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