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.

doi:10.1016/j.jctb.2012.08.002

arXiv 2008-10-26 DOI 10.1016/j.jctb.2012.08.002 0 مشاهدة

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.

Combinatorics Mathematical Physics 05C15 (Primary), 05A20, 05B35, 05C99, 05E99, 30C15, 82B20 (Secondary)

الأصل · EN

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 (cond-mat/9904146) 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.

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