Title: Statistical Mechanics and the Tutte Polynomial
Speaker: Nathan Hayford
Date/Time: Friday, January 28th, 2:00 pm
Abstract: The Tutte polynomial is a well-known graph invariant, from which many important graph-theoretic properties can be read off. We discuss the equivalence of this polynomial to an important model in statistical physics: the q-Potts model, which is a generalization of the simplistic model of a magnet (the Ising model). We use this equivalence to develop the well-known high-temperature expansion of the Potts model. Furthermore, we discuss what we can learn about graph theory from statistical mechanics, and vice versa.