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 J xy . We also prove some further inequalities, and obtain exact asymptotics for τ2 at low temperatures.
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Mathematics Subject Classification (2000): 60K35, 82C20
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Nacu, Ş. Glauber dynamics on the cycle is monotone. Probab. Theory Relat. Fields 127, 177–185 (2003). https://doi.org/10.1007/s00440-003-0279-x
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DOI: https://doi.org/10.1007/s00440-003-0279-x