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Random cluster dynamics for the Ising model is rapidly mixing

With Mark Jerrum (Queen Mary, London)

Random cluster dynamics for the Ising model is rapidly 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 also runs in polynomial time, at any temperature, with the same time bound. (Joint work with Heng Guo, Edinburgh.)

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