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

Levin, D, Luczak, Malwina and Peres, Y (2007) Glauber dynamics for the mean-field Ising model: cut-off, critical power law, and metastability. LSE-CDAM-2007-35. London school of economics and political science, London, UK.

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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 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).

Item Type: Monograph (Report)
Official URL: http://www.cdam.lse.ac.uk/Reports/
Additional Information: © 2007 London school of economics and political science
Library of Congress subject classification: H Social Sciences > H Social Sciences (General)
Sets: Departments > Mathematics
Research centres and groups > Computational, Discrete and Applicable Mathematics@LSE (CDAM)
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Identification Number: LSE-CDAM-2007-35
Date Deposited: 10 Jul 2008 09:25
URL: http://eprints.lse.ac.uk/6796/

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