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 journalArticle

    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
    Volume87
    Issue number1
    DOIs
    StatePublished - Jan 24 2013

    Fingerprint

    Quadrangulation
    Long-range Order
    Antiferromagnet
    triangulation
    Transfer Matrix
    Finite Temperature
    Triangulation
    sublattices
    Phase Transition
    Monte Carlo Simulation
    Graph in graph theory
    simulation
    temperature
    Family

    ASJC Scopus subject areas

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

    Cite this

    Huang, Y., Chen, K., Deng, Y., Jacobsen, J. L., Kotecký, R., Salas, J., ... Swart, J. M. (2013). Two-dimensional Potts antiferromagnets with a phase transition at arbitrarily large q. Physical Review E, 87(1), [012136]. https://doi.org/10.1103/PhysRevE.87.012136

    Two-dimensional Potts antiferromagnets with a phase transition at arbitrarily large q. / Huang, Yuan; Chen, Kun; Deng, Youjin; Jacobsen, Jesper Lykke; Kotecký, Roman; Salas, Jesús; Sokal, Alan D.; Swart, Jan M.

    In: Physical Review E, Vol. 87, No. 1, 012136, 24.01.2013.

    Research output: Contribution to journalArticle

    Huang, Y, Chen, K, Deng, Y, Jacobsen, JL, Kotecký, R, Salas, J, Sokal, AD & Swart, JM 2013, 'Two-dimensional Potts antiferromagnets with a phase transition at arbitrarily large q', Physical Review E, vol. 87, no. 1, 012136. https://doi.org/10.1103/PhysRevE.87.012136
    Huang Y, Chen K, Deng Y, Jacobsen JL, Kotecký R, Salas J et al. Two-dimensional Potts antiferromagnets with a phase transition at arbitrarily large q. Physical Review E. 2013 Jan 24;87(1). 012136. https://doi.org/10.1103/PhysRevE.87.012136
    Huang, Yuan ; Chen, Kun ; Deng, Youjin ; Jacobsen, Jesper Lykke ; Kotecký, Roman ; Salas, Jesús ; Sokal, Alan D. ; Swart, Jan M. / Two-dimensional Potts antiferromagnets with a phase transition at arbitrarily large q. In: Physical Review E. 2013 ; Vol. 87, No. 1.
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