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