Absence of phase transition for antiferromagnetic Potts models via the Dobrushin uniqueness theorem

Jeśus Salas, Alan D. Sokal

    Research output: Contribution to journalArticle

    Abstract

    We prove that the q-state Potts antiferromagnet on a lattice of maximum coordination number r exhibits exponential decay of correlations uniformly at all temperatures (including zero temperature) whenever q>2r. We also prove slightly better bounds for several two-dimensional lattices: square lattice (exponential decay for q≥7), triangular lattice (q≥11), hexagonal lattice (q≥4), and Kagomé lattice (q≥6). The proofs are based on the Dobrushin uniqueness theorem.

    Original languageEnglish (US)
    Pages (from-to)551-579
    Number of pages29
    JournalJournal of Statistical Physics
    Volume86
    Issue number3-4
    DOIs
    StatePublished - Feb 1997

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    Keywords

    • Antiferromagnetic Potts models
    • Dobrushin uniqueness theorem
    • Phase transition

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Mathematical Physics

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