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


    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
    Issue number1
    StatePublished - Jan 1 2013



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

    ASJC Scopus subject areas

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

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