CDAM: Computational, Discrete and Applicable Mathematics@LSE

CDAM Research Report, LSE-CDAM-2007-35

February 2008

Glauber Dynamics for the Mean-Field Ising Model: Cut-Off, Critical Power Law, and Metastability

David A. Levin, Malwina J. Luczak, and Yuval Peres

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).

A PDF file (216 kB) with the full contents of this report can be downloaded by clicking here.

Alternatively, if you would like to get a free hard copy of this report, please send the number of this report, LSE-CDAM-2007-35, together with your name and postal address to:

CDAM Research Reports Series
Centre for Discrete and Applicable Mathematics
London School of Economics
Houghton Street
London WC2A 2AE, U.K.

Phone: +44(0)-20-7955 7494.
Fax: +44(0)-20-7955 6877.
Email: info@maths.lse.ac.uk

		Introduction to the CDAM Research Report Series.
		CDAM Homepage.

		CDAM Research Reports Series Centre for Discrete and Applicable Mathematics London School of Economics Houghton Street London WC2A 2AE, U.K.
		Phone: +44(0)-20-7955 7494. Fax: +44(0)-20-7955 6877. Email: info@maths.lse.ac.uk