Absence of Phase Transition for Antiferromagnetic Potts Models via the Dobrushin Uniqueness Theorem

Details Absence of Phase Transition for Antiferromagnetic Potts Models via the Dobrushin Uniqueness Theorem Absence of Phase Transition for Antiferromagnetic Potts Models via the Dobrushin Uniqueness Theorem

1996-03-08

arxiv.org/abs/cond-mat/9603068v1

J.Statist.Phys. 86 (1997) 551-579

Physics

Condensed Matter

32 pages including 3 figures. Self-unpacking file containing the tex file, the needed macros (epsf.sty, indent.sty, subeqnarra

Scientific paper

10.1007/BF02199113

We prove that the $q$-state Potts antiferromagnet on a lattice of maximum coordination number $r$ exhibits exponential decay of correlations uniformly at all temperatures (including zero temperature) whenever $q > 2r$. We also prove slightly better bounds for several two-dimensional lattices: square lattice (exponential decay for $q \ge 7$), triangular lattice ($q \ge 11$), hexagonal lattice ($q \ge 4$), and Kagom\'e lattice ($q \ge 6$). The proofs are based on the Dobrushin uniqueness theorem.

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