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

作者：Jackson Bill^*; Procacci Aldo; Sokal Alan D

来源：Journal of Combinatorial Theory - Series B, 2013, 103(1): 21-45.

DOI：10.1016/j.jctb.2012.08.002

• Graph
• Chromatic polynomial
• Multivariate Tutte polynomial
• Potts model
• Penrose identity
• Penrose inequality
• Lambert W function

We find zero-free regions in the complex plane at large vertical bar q vertical bar 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 (2001) [28] that applies only within the complex antiferromagnetic regime vertical bar 1 + W-e vertical bar %26lt;= 1. Our proof uses the polymer-gas representation of the multivariate Tutte polynomial together with the Penrose identity.

• 出版日期2013-1