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Long-Time Behavior for the 1-D Stochastic Ising Model with Unbounded Random Couplings

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Abstract

We consider the ferromagnetic Ising model with Glauber spin flip dynamics in one dimension. The external magnetic field vanishes and the couplings are i.i.d. random variables. If their distribution has compact support, the disorder averaged spin auto-correlation function has an exponential decay in time. We prove that, if the couplings are unbounded, the decay switches to either a power law or a stretched exponential, in general.

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Authors and Affiliations

  1. Zentrum Mathematik, Technische Universität München, D-85747, Garching, Germany

    H. Spohn

  2. Institute for Information Transmission Problems, Bolshoy Karetny per. 19, o101447, Moscow, Russia

    E. Zhizhina

Authors
  1. H. Spohn
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  2. E. Zhizhina
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Spohn, H., Zhizhina, E. Long-Time Behavior for the 1-D Stochastic Ising Model with Unbounded Random Couplings. Journal of Statistical Physics 111, 419–431 (2003). https://doi.org/10.1023/A:1022225612366

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  • DOI: https://doi.org/10.1023/A:1022225612366

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