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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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