London, E1 4NS\
    viresh.s.patel@gmail.com
date:  
title: Mixing of the Glauber dynamics for the ferromagnetic Potts model
---

Introduction
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The Potts model was introduced in 1952 [@pot52] as a generalisation of the Ising model of magnetism. The Potts model has been extensively studied not only in statistical physics, but also in computer science, mathematics and further afield. In physics the main interest is in studying phase transitions and modelling the evolution of non-equilibrium particle systems; see [@wu82] for a survey. In computer science, the Potts model is a test-bed for approximation algorithms and techniques. It has also been heavily studied in the areas of discrete mathematics and graph theory, through an equivalence to the Tutte polynomial of a graph [@wel93], and thereby links to the chromatic polynomial and many other graph invariants. The Potts model and its extensions have also appeared many times in the social sciences, for example in modelling financial markets [@voi01] and voter interaction in social networks [@cho07], and in biology [@gla92].

[**Potts Model.**]{}  In graph-theoretic language, the Potts model assigns a weight to each possible colouring of a graph (not necessarily proper), and we are interested in sampling from the distribution induced by the weights. The 