Random Field Induced Order in Low Dimension I
  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. 
Nicholas Crawford
math-ph cond-mat.stat-mech math.MP math.PR