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

Levin, David A., Luczak, Malwina J. and Peres, Yuval (2010) Glauber dynamics for the mean-field Ising model: cut-off, critical power law, and metastability. Probability Theory and Related Fields, 146 (1-2). pp. 223-265. ISSN 0178-8051

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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).

Item Type: Article
Official URL: http://www.springer.com/mathematics/probability/jo...
Additional Information: © 2010 Springer
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 01 Dec 2010 12:18
URL: http://eprints.lse.ac.uk/29589/

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