Two-dimensional Potts antiferromagnets with a phase transition at arbitrarily large q

Yuan Huang, Kun Chen, Youjin Deng, Jesper Lykke Jacobsen, Roman Kotecký, Jesús Salas, Alan D. Sokal, Jan M. Swart

    Research output: Contribution to journalArticlepeer-review

    Abstract

    We exhibit infinite families of two-dimensional lattices (some of which are triangulations or quadrangulations of the plane) on which the q-state Potts antiferromagnet has a finite-temperature phase transition at arbitrarily large values of q. This unexpected result is proven rigorously by using a Peierls argument to measure the entropic advantage of sublattice long-range order. Additional numerical data are obtained using transfer matrices, Monte Carlo simulation, and a high-precision graph-theoretic method.

    Original languageEnglish (US)
    Article number012136
    JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
    Volume87
    Issue number1
    DOIs
    StatePublished - Jan 24 2013

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Statistics and Probability
    • Condensed Matter Physics

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