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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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