Graphical Abstract “Science is fun because it can take us one step closer to understanding the world … My favorite musician Alecia Beth Moore (aka Pink) …” Find out more about Nana Wang in her Introducing Profile.

We show that the mixing time of Glauber (single edge update) dynamics for the random cluster model at q = 2 is bounded by a polynomial in the size of the underlying graph. As a consequence, the Swendsen-Wang algorithm for the ferromagnetic Ising model at any temperature has the same polynomial mixing time bound.

We study two widely used algorithms for the Potts model on rectangular subsets of the hypercubic lattice Zd – heat bath dynamics and the Swendsen-Wang algorithm – and prove that, under certain circumstances, the mixing in these algorithms is torpid or slow. In particular, we show that for heat bath dynamics throughout the region of phase coexistence, and for the Swendsen-Wang algorithm at the t...