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

TL;DR

This paper introduces a mechanism where random fields induce order in classical and quantum systems, challenging the traditional understanding of the Mermin-Wagner-Hohenberg effect, with potential realizations in ultracold atomic gases.

Contribution

It rigorously proves spontaneous magnetization in a 2D classical XY model with a uniaxial random field and discusses extensions to quantum systems and experimental realizations.

Findings

Proved spontaneous magnetization at T=0 in the 2D XY model with random field

Provided evidence for order at small positive temperatures

Suggested experimental setups with ultracold atoms for RFIO

Abstract

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.