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

Abstract

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 Kagomé lattice ($q\ge 6$). The proofs are based on the Dobrushin uniqueness theorem.

Comments: 32 pages including 3 figures. Self-unpacking file containing the tex file, the needed macros (epsf.sty, indent.sty, subeqnarray.sty, and eqsection.sty) and the 3 ps files