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
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).
|Additional Information:||© 2010 Springer|
|Uncontrolled Keywords:||Markov chains, Ising model, Curie–Weiss model, mixing time, cut-off, coupling, glauber dynamics, metastability, heat-bath dynamics, mean-field model|
|Library of Congress subject classification:||Q Science > QA Mathematics|
|Sets:||Departments > Mathematics|
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