Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. III. Triangular-Lattice Chromatic Polynomial

Jesper Lykke Jacobsen, Jesús Salas, Alan D. Sokal

    Research output: Contribution to journalArticle

    Abstract

    We study the chromatic polynomial P G(q) for m ≤ n triangular-lattice strips of widths m ≤ 12 P, 9 F (with periodic or free transverse boundary conditions, respectively) and arbitrary lengths n (with free longitudinal boundary conditions). The chromatic polynomial gives the zero-temperature limit of the partition function for the q-state Potts antiferromagnet. We compute the transfer matrix for such strips in the Fortuin-Kasteleyn representation and obtain the corresponding accumulation sets of chromatic zeros in the complex q-plane in the limit n → ∞. We recompute the limiting curve obtained by Baxter in the thermodynamic limit m, n → ∞ and find new interesting features with possible physical consequences. Finally, we analyze the isolated limiting points and their relation with the Beraha numbers.

    Original languageEnglish (US)
    Pages (from-to)921-1017
    Number of pages97
    JournalJournal of Statistical Physics
    Volume112
    Issue number5-6
    DOIs
    StatePublished - Sep 2003

    Keywords

    • Antiferromagnetic Potts model
    • Beraha numbers
    • Beraha-Kahane-Weiss theorem
    • Chromatic polynomial
    • Chromatic root
    • Fortuin-Kasteleyn representation
    • Transfer matrix
    • Triangular lattice

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Mathematical Physics

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