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

By D Levin, Malwina Luczak and Y Peres

Abstract

We study the Glauber dynamics for the Ising model on the complete graph, also known as the Curie-Weiss Model. For β < 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-β)]-1 n log n. For β = 1, we prove that the mixing time is of order n3/2. 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)

Topics: H Social Sciences (General)
Publisher: London school of economics and political science
Year: 2007
OAI identifier: oai:eprints.lse.ac.uk:6796
Provided by: LSE Research Online
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