%0 Journal Article
%T Random Field Induced Order in Low Dimension I
%A Nicholas Crawford
%J Mathematics
%D 2012
%I arXiv
%X 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 $\Z^3$ 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.
%U http://arxiv.org/abs/1208.3149v2