Rapid Mixing for Lattice Colorings with Fewer Colors
Statistical Mechanics
2015-06-25 v1
Abstract
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.
Cite
@article{arxiv.cond-mat/0508737,
title = {Rapid Mixing for Lattice Colorings with Fewer Colors},
author = {Dimitris Achlioptas and Michael Molloy and Cristopher Moore and Frank Van Bussell},
journal= {arXiv preprint arXiv:cond-mat/0508737},
year = {2015}
}
Comments
Appeared in Proc. LATIN 2004, to appear in JSTAT