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

By David A. Levin, Malwina J. Luczak and Yuval 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 n 3/2. 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: QA Mathematics
Publisher: Springer
Year: 2010
DOI identifier: 10.1007/s00440-008-0189-z
OAI identifier: oai:eprints.lse.ac.uk:29589
Provided by: LSE Research Online
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