Mixing time for the solid-on-solid model

We analyze the mixing time of a natural local Markov chain (the Glauber dynamics) on configurations of the solid-on-solid model of statistical physics. This model has been proposed, among other things, as an idealization of the behavior of contours in the Ising model at low temperatures. Our main result is an upper bound on the mixing time of O~(n3.5), which is tight within a factor of O~(√n). The proof, which in addition gives insight into the actual evolution of the contours, requires the introduction of several novel analytical techniques that we conjecture will have other applications.

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