Glauber Dynamics On The Cycle Is Monotone
Abstract
We study heat-bath Glauber dynamics for the ferromagnetic Ising model on a finite cycle (a graph where every vertex has degree two). We prove that the relaxation time τ2 is an increasing function of any of the couplings Jxy. We also prove some further inequalities, and obtain exact asymptotics for τ2 at low temperatures.
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