Random Cluster Dynamics at q = 2 is Fast Mixing

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.

Joint work with Mark Jerrum.

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