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

Authors:
Bill Jackson;Aldo Procacci;Alan D. Sokal
Affiliations:
School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom;Departamento de Matemática, Universidade Federal de Minas Gerais, Av. Antônio Carlos, 6627 - Caixa Postal 702, 30161-970 Belo Horizonte, MG, Brazil;Department of Physics, New York University, 4 Washington Place, New York, NY 10003, USA
Venue:
Journal of Combinatorial Theory Series B
Year:
2013

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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) Z"G(q,w) of a graph G with general complex edge weights w={w"e}. This generalizes a result of Sokal (2001) [28] that applies only within the complex antiferromagnetic regime |1+w"e|=