Complex zero-free regions at large |q| for multivariate Tutte polynomials (alias Potts-model partition functions) with general complex edge weights
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.
Keywords
Cite
@article{arxiv.0810.4703,
title = {Complex zero-free regions at large |q| for multivariate Tutte polynomials (alias Potts-model partition functions) with general complex edge weights},
author = {Bill Jackson and Aldo Procacci and Alan D. Sokal},
journal= {arXiv preprint arXiv:0810.4703},
year = {2014}
}
Comments
LaTeX2e, 34 pages. Version 2 improves Theorem 1.3, using an improved Proposition 4.4 and a new Proposition 5.2. Version 3 (published in JCTB) makes many improvements: Theorems 1.2 and 1.3 are strengthened; the bounds of Section 5 are generalized to allow vertex weights; the discussion in Section 6 and examples in Section 7 are re-thought