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

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

    Research output: Contribution to journalArticle

    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.

    Original languageEnglish (US)
    Pages (from-to)1339-1394
    Number of pages56
    JournalCommunications in Mathematical Physics
    Volume330
    Issue number3
    DOIs
    StatePublished - 2014

    Fingerprint

    Potts Model
    Phase Transition
    Entropy
    entropy
    Quadrangulation
    Long-range Order
    Antiferromagnet
    Gibbs Measure
    Magnetization
    sublattices
    apexes
    Lower bound
    magnetization
    Zero
    temperature

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Mathematical Physics

    Cite this

    Entropy-Driven Phase Transition in Low-Temperature Antiferromagnetic Potts Models. / Kotecký, Roman; Sokal, Alan D.; Swart, Jan M.

    In: Communications in Mathematical Physics, Vol. 330, No. 3, 2014, p. 1339-1394.

    Research output: Contribution to journalArticle

    Kotecký, Roman ; Sokal, Alan D. ; Swart, Jan M. / Entropy-Driven Phase Transition in Low-Temperature Antiferromagnetic Potts Models. In: Communications in Mathematical Physics. 2014 ; Vol. 330, No. 3. pp. 1339-1394.
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