Complex zero-free regions at large |q| for multivariate Tutte   polynomials (alias Potts-model partition functions) with general complex edge   weights
  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. 
Bill Jackson, Aldo Procacci and Alan D. Sokal