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

    Fingerprint

    Chromatic Polynomial
    Triangular Lattice
    Matrix Function
    Potts Model
    Transfer Matrix
    Partition Function
    Transfer Function
    Strip
    partitions
    polynomials
    Limiting
    Boundary conditions
    Antiferromagnet
    strip
    Zero
    Thermodynamic Limit
    boundary conditions
    Transverse
    Curve
    Arbitrary

    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

    • Physics and Astronomy(all)
    • Statistical and Nonlinear Physics
    • Mathematical Physics

    Cite this

    Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. III. Triangular-Lattice Chromatic Polynomial. / Jacobsen, Jesper Lykke; Salas, Jesús; Sokal, Alan D.

    In: Journal of Statistical Physics, Vol. 112, No. 5-6, 09.2003, p. 921-1017.

    Research output: Contribution to journalArticle

    Jacobsen, Jesper Lykke ; Salas, Jesús ; Sokal, Alan D. / Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. III. Triangular-Lattice Chromatic Polynomial. In: Journal of Statistical Physics. 2003 ; Vol. 112, No. 5-6. pp. 921-1017.
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