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

TL;DR

This paper establishes large complex zero-free regions for the multivariate Tutte polynomial, extending previous results to more general complex edge weights using polymer-gas representations and the Penrose identity.

Contribution

It generalizes existing zero-free region results for the Tutte polynomial to broader complex weights using novel combinatorial methods.

Findings

Identifies large zero-free regions in the complex plane for the Tutte polynomial.

Extends previous antiferromagnetic regime results to general complex weights.

Uses polymer-gas representation and Penrose identity for proofs.

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 (cond-mat/9904146) that applies only within the complex antiferromagnetic regime |1+w_e| \le 1. Our proof uses the polymer-gas representation of the multivariate Tutte polynomial together with the Penrose identity.