Jes\'us Salas and Alan D. Sokal
Absence of Phase Transition for Antiferromagnetic Potts Models
via the Dobrushin Uniqueness Theorem.
(396K, PostScript file)
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.