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Glauber Dynamics On The Cycle Is Monotone

Serban Nacu
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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 $τ_2$ is an increasing function of any of the couplings $J_{xy}$. We also prove some further inequalities, and obtain exact asymptotics for $τ_2$ at low temperatures.

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Serban Nacu. 2003-05-03. Glauber Dynamics On The Cycle Is Monotone. https://arxiv.org/abs/math/0305056

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