Entropy-Driven Phase Transition in Low-Temperature Antiferromagnetic Potts Models

Roman Kotecký, Alan D. Sokal, Jan M. Swart

    Research output: Contribution to journalArticlepeer-review


    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.

    Original languageEnglish (US)
    Pages (from-to)1339-1394
    Number of pages56
    JournalCommunications In Mathematical Physics
    Issue number3
    StatePublished - Sep 2014

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Mathematical Physics


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