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Journal Article

Entropy-driven phase transition in low-temperature antiferromagnetic Potts models

Kotecký R., Sokal A.D., Swart Jan M.

: Communications in Mathematical Physics vol.330, 3 (2014), p. 1339-1394

: GA201/09/1931, GA ČR, GAP201/12/2613, GA ČR

: Antiferromagnetic Potts model, proper coloring, plane quadrangulation, phase transition, diced lattice

: 10.1007/s00220-014-2005-1


(eng): We prove the existence of long-range order at sufficiently low temperatures, including zero temperature, for the three-state Potts antiferromagnet on a class of quasi-transitive plane quadrangulations, including the diced lattice. More precisely, we show the existence of (at least) three infinite-volume Gibbs measures, which exhibit spontaneous magnetization in the sense that vertices in one sublattice have a higher probability to be in one state than in either of the other two states. For the special case of the diced lattice, we give a good rigorous lower bound on this probability, based on computer-assisted calculations that are not available for the other lattices.

: BA