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On the Decay of Correlations in the Random Field Ising Model

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Abstract

In a celebrated 1990 paper, Aizenman and Wehr proved that the two-dimensional random field Ising model has a unique infinite volume Gibbs state at any temperature. The proof is ergodic-theoretic in nature and does not provide any quantitative information. This article proves the first quantitative version of the Aizenman–Wehr theorem. The proof introduces a new method for proving decay of correlations that may be interesting in its own right. A fairly detailed sketch of the main ideas behind the proof is also included.

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Authors and Affiliations

  1. Department of Statistics, Stanford University, Sequoia Hall, 390 Serra Mall, Stanford, CA, 94305, USA

    Sourav Chatterjee

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  1. Sourav Chatterjee
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Correspondence to Sourav Chatterjee.

Additional information

Communicated by H. Spohn

Research partially supported by NSF grant DMS-1608249.

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Chatterjee, S. On the Decay of Correlations in the Random Field Ising Model. Commun. Math. Phys. 362, 253–267 (2018). https://doi.org/10.1007/s00220-018-3085-0

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  • DOI: https://doi.org/10.1007/s00220-018-3085-0

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