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

摘要

We study the Glauber dynamics for the Ising model on the complete graph, also known as the Curie–Weiss Model. For β 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). Keywords Markov chains - Ising model - Curie–Weiss model - Mixing time - Cut-off - Coupling - Glauber dynamics - Metastability - Heat-bath dynamics - Mean-field model Mathematics Subject Classification (2000) 60J10 - 60K35 - 82C20 Research of Y. Peres was supported in part by NSF grant DMS-0605166.