Random field induced order in low dimension

We address an unresolved issue in the physics of low-dimensional many-body systems: the question of whether or not a random field can produce order at low temperatures for statistical mechanical systems possessing continuous internal symmetries. Concretely, we verify that the XY model in a uniaxial random field orders in two and three dimensions. The direction the system orders is perpendicular to the randomness for any choice of symmetry breaking field with nonzero projection perpendicular to the randomness. The result is particularly relevant in two dimensions, where there are a number of competing effects -quasi-long-range order of the pure system and strong fluctuations of the random field. While we consider only classical systems explicitly, the effect is robust and our work has implications for quantum systems as well, producing ordered phases in any dimension. Copyright (C) EPLA, 2013