Transfer matrices and partition-function zeros for zntiferromagnetic potts models: VV. further results for the square-lattice chromatic polynomial

Jesús Salas, Alan D. Sokal

    Research output: Contribution to journalArticle

    Abstract

    We derive some new structural results for the transfer matrix of square-lattice Potts models with free and cylindrical boundary conditions. In particular, we obtain explicit closed-form expressions for the dominant (at large |q|) diagonal entry in the transfer matrix, for arbitrary widths m, as the solution of a special one-dimensional polymer model. We also obtain the large-q expansion of the bulk and surface (resp. corner) free energies for the zero-temperature antiferromagnet (= chromatic polynomial) through order q -47 (resp. q -46). Finally, we compute chromatic roots for strips of widths 12 with free boundary conditions and locate roughly the limiting curves.

    Original languageEnglish (US)
    Pages (from-to)279-373
    Number of pages95
    JournalJournal of Statistical Physics
    Volume135
    Issue number2
    DOIs
    Publication statusPublished - Apr 2009

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    Keywords

    • Antiferromagnetic Potts model
    • Beraha-Kahane-Weiss theorem
    • Chromatic polynomial
    • Chromatic root
    • Finite-lattice method
    • Fortuin-Kasteleyn representation
    • Large-q expansion
    • One-dimensional polymer model
    • Square lattice
    • Transfer matrix

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Mathematical Physics

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