We consider the performance of Glauber dynamics for the random cluster model (with q>1). On the random regular graph, the model exhibits the ordered/disordered transition which causes bottlenecks in an interval of temperatures (for q>2). This impedes fast mixing from worst-case starting configurations, for both local and non-local Markov chains. Nevertheless, it is widely conjectured that the bottlenecks can be avoided by initialising the chain more judiciously.
Our main result establishes this conjecture for all sufficiently large q (with respect to the degree Δ). Specifically, we consider the mixing time of Glauber dynamics initialised from the two extreme configurations, and obtain a pair of fast mixing bounds which cover all temperatures, including in particular the bottleneck window.
Joint with L. Goldberg and P. Smolarova.