Fast mixing for independent sets, colorings, and other models on trees

We study the mixing time of the Glauber dynamics for general spin systems on bounded-degree trees, including the Ising model, the hard-core model (independent sets) and the antiferromagnetic Potts model at zero temperature (colorings). We generalize a framework, developed in our recent paper [18] in the context of the Ising model, for establishing mixing time O(n log n), which ties this property closely to phase transitions in the underlying model. We use this framework to obtain rapid mixing results for several models over a significantly wider range of parameter values than previously known, including situations in which the mixing time is strongly dependent on the boundary condition.

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