Condensation in the inhomogeneous zero-range process: an interplay between interaction and diffusion disorder

TL;DR

This paper investigates how the combination of on-site interactions and inhomogeneous diffusion influences condensation in the zero-range process, revealing a universal phase diagram and a novel extended condensed phase with unique properties.

Contribution

It introduces a universal phase diagram for condensation in the zero-range process considering interaction and disorder, and identifies a new extended condensed phase with unique spatial characteristics.

Findings

Existence of a universal phase diagram in the interaction-disorder plane.

Identification of an extended condensed phase with a condensate at any site of a large favored set.

The extended phase interpolates between spontaneous and explicit symmetry breaking.

Abstract

We analyze the role of the interplay between on-site interaction and inhomogeneous diffusion on the phenomenon of condensation in the zero-range process. We predict a universal phase diagram in the plane of two exponents, respectively characterizing the interactions and the diffusion disorder. The most prominent outcome is the existence of an extended condensed phase. In the latter phase, which originates as a result of the combined effects of strong enough interaction and weak enough disorder, a typical high-density configuration has a unique condensate on top of a critical background, but the condensate may be located at any site of a large hosting set of favored sites, whose size grows sub-extensively. The novel extended condensed phase thus interpolates continuously between the two scenarios associated so far with the condensation transition, namely spontaneous symmetry breaking and explicit symmetry breaking.