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Random Field Induced Order in Low Dimension I

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Abstract

Consider the classical XY model in a weak random external field pointing along the Y axis with strength \({\epsilon}\). We prove that the model defined on \({\mathbb{Z}^3}\) with nearest neighbor coupling exhibits residual magnetic order in the horizontal direction for arbitrarily weak random field strengths and, depending on field strength, sufficiently low temperature.

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Authors and Affiliations

  1. Department of Mathematics, The Technion, Haifa, Israel

    Nicholas Crawford

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  1. Nicholas Crawford
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Correspondence to Nicholas Crawford.

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Communicated by F. Toninelli

Supported in part at the Technion by a Marilyn and Michael Winer Fellowship and a Landau Fellowship.

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Crawford, N. Random Field Induced Order in Low Dimension I. Commun. Math. Phys. 328, 203–249 (2014). https://doi.org/10.1007/s00220-014-1979-z

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  • DOI: https://doi.org/10.1007/s00220-014-1979-z

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