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) ZG(q,w) of a graph G with general complex edge weights w={we}. This generalizes a result of Sokal (2001) [28] 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.
Original language | English (US) |
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Pages (from-to) | 21-45 |
Number of pages | 25 |
Journal | Journal of Combinatorial Theory. Series B |
Volume | 103 |
Issue number | 1 |
DOIs | |
State | Published - Jan 2013 |
Keywords
- Chromatic polynomial
- Graph
- Lambert w function
- Multivariate tutte polynomial
- Penrose identity
- Penrose inequality
- Potts model
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics