Cdam Lse-cdam-2007-35 Glauber Dynamics for the Mean-field Ising Model: Cut-off, Critical Power Law, and Metastability
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چکیده
A. 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)]−1n 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).
منابع مشابه
Glauber Dynamics for the Mean-field Ising Model: Cut-off, Critical Power Law, and Metastability
A. 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)]−1n log n. For β = 1, we prove that the mixing time is of order n3/2. For β > 1, we study metastability. In particula...
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تاریخ انتشار 2008