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Glauber dynamics on the cycle is monotone
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  • Published: 18 June 2003

Glauber dynamics on the cycle is monotone

  • Şerban Nacu1 

Probability Theory and Related Fields volume 127, pages 177–185 (2003)Cite this article

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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 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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References

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Authors and Affiliations

  1. University of California, Berkeley, USA

    Şerban Nacu

Authors
  1. Şerban Nacu
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Correspondence to Şerban Nacu.

Additional information

Mathematics Subject Classification (2000): 60K35, 82C20

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Cite this article

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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  • Received: 16 December 2002

  • Revised: 26 March 2003

  • Published: 18 June 2003

  • Issue Date: October 2003

  • DOI: https://doi.org/10.1007/s00440-003-0279-x

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Keywords

  • Relaxation Time
  • Ising Model
  • Glauber Dynamic
  • Exact Asymptotics
  • Ferromagnetic Ising Model
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