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

Levin, David A.; Luczak, Malwina J.; Peres, Yuval

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

Authors

Levin, David A.

Luczak, Malwina J.

Peres, Yuval

Description

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).
40 pages