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We study the Glauber dynamics for the Ising model on the complete graph, alsoknown as the Curie-Weiss Model. For beta < 1, we prove that the dynamicsexhibits a cut-off: the distance to stationarity drops from near 1 to near 0 ina window of order n centered at [2(1-beta)]^{-1} n log n. For beta = 1, weprove that the mixing time is of order n^{3/2}. For beta > 1, we studymetastability. In particular, we show that the Glauber dynamics restricted tostates of non-negative magnetization has mixing time O(n log n).

Glauber dynamics for the mean-field Ising model: cut-off, critical power law, and metastability