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Exponential Decay of Correlations in the 2D Random Field Ising Model

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Abstract

An extension of the Ising spin configurations to continuous functions is used for an exact representation of the random field Ising model’s order parameter in terms of disagreement percolation. This facilitates an extension of the recent analyses of the decay of correlations to positive temperatures, at homogeneous but arbitrarily weak disorder.

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Acknowledgements

We gratefully acknowledge the following support. The work of MA was supported in parts by the NSF Grant DMS-1613296, and the Weston Visiting Professorship at the Weizmann Institute of Science. The work of MH and RP was supported in part by Israel Science Foundation Grant 861/15 and the European Research Council starting Grant 678520 (LocalOrder). MH was supported by the Zuckerman Postdoctoral Fellowship. We thank the Faculty of Mathematics and Computer Science and the Faculty of Physics at WIS for the hospitality enjoyed there during work on this project.

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Authors and Affiliations

  1. Departments of Mathematics and Physics, Princeton University, Princeton, NJ, 08544, USA

    Michael Aizenman

  2. Weizmann Institute of Science, Rehovot, Israel

    Michael Aizenman

  3. School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel

    Matan Harel & Ron Peled

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  1. Michael Aizenman
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  2. Matan Harel
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  3. Ron Peled
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Correspondence to Michael Aizenman.

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Communicated by Juerg Martin Froehlich.

To Joel, inspiring mentor and friend

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Aizenman, M., Harel, M. & Peled, R. Exponential Decay of Correlations in the 2D Random Field Ising Model. J Stat Phys 180, 304–331 (2020). https://doi.org/10.1007/s10955-019-02401-5

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