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

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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Correspondence to Michael Aizenman.

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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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Keywords

  • Random field Ising model
  • Quenched disorder
  • 2D
  • Disagreement percolation
  • Exponential decay
  • Anti-concentration bounds