Disorder versus the Mermin-Wagner-Hohenberg effect: From classical spin systems to ultracold atomic gases

We propose a general mechanism of random-field-induced order (RFIO), in whichlong-range order is induced by a random field that breaks the continuoussymmetry of the model. We particularly focus on the case of the classicalferromagnetic XY model on a 2D lattice, in a uniaxial random field. We proverigorously that the system has spontaneous magnetization at temperature T=0,and we present strong evidence that this is also the case for small T>0. Wediscuss generalizations of this mechanism to various classical and quantumsystems. In addition, we propose possible realizations of the RFIO mechanism,using ultracold atoms in an optical lattice. Our results shed new light oncontroversies in existing literature, and open a way to realize RFIO withultracold atomic systems.Comment: published version; 8 pages, 3 figure