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

H. Spohn; E. Zhizhina

doi:10.1023/A:1022225612366

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

H. Spohn, E. Zhizhina

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Institute for Information Transmission Problems of the Russian Academy of Sciences

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1 Scopus citations

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.

Original language	English
Pages (from-to)	419-431
Number of pages	13
Journal	Journal of Statistical Physics
Volume	111
Issue number	1-2
DOIs	https://doi.org/10.1023/A:1022225612366
State	Published - Apr 2003

Keywords

Disordered energy
Spin-flip dynamics
Stretched exponential decay

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10.1023/A:1022225612366

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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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AB - 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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KW - Spin-flip dynamics

KW - Stretched exponential decay

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

Abstract

Keywords

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