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Random cluster dynamics for the Ising model is rapidly mixing

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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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