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Glauber dynamics on the cycle is monotone. (English) Zbl 1068.82014
Summary: 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 \(\tau_2\) is an increasing function of any of the couplings \(J_{xy} \). We also prove some further inequalities, and obtain exact asymptotics for \(\tau_2\) at low temperatures.

MSC:
82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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