Complex zero-free regions at large |q| for multivariate Tutte polynomials (alias Potts-model partition functions) with general complex edge weights

Bill Jackson, Aldo Procacci, Alan D. Sokal

    Research output: Contribution to journalArticle

    Abstract

    We find zero-free regions in the complex plane at large |. q| for the multivariate Tutte polynomial (also known in statistical mechanics as the Potts-model partition function) ZG(q,w) of a graph G with general complex edge weights w={we}. This generalizes a result of Sokal (2001) [28] that applies only within the complex antiferromagnetic regime |1+we|≤1. Our proof uses the polymer-gas representation of the multivariate Tutte polynomial together with the Penrose identity.

    Original languageEnglish (US)
    Pages (from-to)21-45
    Number of pages25
    JournalJournal of Combinatorial Theory, Series B
    Volume103
    Issue number1
    DOIs
    StatePublished - Jan 2013

    Fingerprint

    Potts model
    Tutte Polynomial
    Polynomial Model
    Multivariate Polynomials
    Potts Model
    Partition Function
    Polynomials
    Statistical mechanics
    Zero
    Statistical Mechanics
    Argand diagram
    Polymers
    Generalise
    Graph in graph theory
    Gases
    Gas

    Keywords

    • Chromatic polynomial
    • Graph
    • Lambert w function
    • Multivariate tutte polynomial
    • Penrose identity
    • Penrose inequality
    • Potts model

    ASJC Scopus subject areas

    • Discrete Mathematics and Combinatorics
    • Theoretical Computer Science
    • Computational Theory and Mathematics

    Cite this

    Complex zero-free regions at large |q| for multivariate Tutte polynomials (alias Potts-model partition functions) with general complex edge weights. / Jackson, Bill; Procacci, Aldo; Sokal, Alan D.

    In: Journal of Combinatorial Theory, Series B, Vol. 103, No. 1, 01.2013, p. 21-45.

    Research output: Contribution to journalArticle

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