  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.
