ABSENCE OF PHASE-TRANSITION FOR ANTIFERROMAGNETIC POTTS MODELS VIA THE DOBRUSHIN UNIQUENESS THEOREM

We prove that the q-state Potts antiferromagnet on a lattice of maximu m coordination number r exhibits exponential decay of correlations uni formly at all temperatures (including zero temperature) whenever q>2r. We also prove slightly better bounds for several two-dimensional latt ices: square lattice (exponential decay for q greater than or equal to 7), triangular lattice (q greater than or equal to 11), hexagonal lat tice (q greater than or equal to 4), and Kagome lattice (q greater tha n or equal to 6). The proofs are based on tile Dobrushin uniqueness th eorem.