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

Kotecký, R; Sokal, AD; Swart, JM; (2012) Entropy-driven phase transition in low-temperature antiferromagnetic Potts models.

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Abstract

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.

Type:Article
Title:Entropy-driven phase transition in low-temperature antiferromagnetic Potts models
Additional information:LaTeX2e, 67 pages. Version 3 is the final version, accepted for publication in Communications in Mathematical Physics
UCL classification:UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Mathematics

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