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

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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) 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. © 2012 Elsevier Inc.

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Jackson, B., Procacci, A., & Sokal, A. D. (2013). Complex zero-free regions at large |q| for multivariate Tutte polynomials (alias Potts-model partition functions) with general complex edge weights. Journal of Combinatorial Theory. Series B, 103(1), 21–45. https://doi.org/10.1016/j.jctb.2012.08.002

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