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

Jan Wehr (1, 2) , Armand Niederberger (1) , Laurent Sanchez-Palencia (3) , Maciej Lewenstein (1, 4)

1 UNIROUEN - Université de Rouen Normandie
2 Department of Mathematics [University of Arizona]
3 laboratoire Charles Fabry de l'Institut d'Optique / Optique atomique
4 ITP - Institut für Theoretische Physik [Hannover]

We propose a general mechanism of random-field-induced order (RFIO), in which long-range order is induced by a random field that breaks the continuous symmetry of the model. We particularly focus on the case of the classical ferromagnetic XY model on a 2D lattice, in a uniaxial random field. We prove rigorously 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. We discuss generalizations of this mechanism to various classical and quantum systems. In addition, we propose possible realizations of the RFIO mechanism, using ultracold atoms in an optical lattice. Our results shed new light on controversies in existing literature, and open a way to realize RFIO with ultracold atomic systems.

Mots clés: disorder; random; spin; ultracold; XY; Heisenberg; optical lattice; Bose-Einstein

Domaines: Autre [cond-mat.other]

Jan Wehr, Armand Niederberger, Laurent Sanchez-Palencia, Maciej Lewenstein. Disorder versus the Mermin-Wagner-Hohenberg effect: From classical spin systems to ultracold atomic gases. Physical Review B: Condensed Matter and Materials Physics (1998-2015), 2006, 74, pp.224448. ⟨10.1103/PhysRevB.74.224448⟩. ⟨hal-00022177v5⟩