96-63 Jes\'us Salas and Alan D. Sokal

Absence of Phase Transition for Antiferromagnetic Potts Models via the Dobrushin Uniqueness Theorem. (396K, PostScript file) Mar 8, 96

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

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