Condensation and symmetry-breaking in the zero-range process with weak site disorder

TL;DR

This paper investigates a zero-range process with weak site disorder, revealing an intermediate condensation phase characterized by a Gamma distribution, and explores fluctuation behaviors confirming a complex phase diagram.

Contribution

It confirms a conjecture that weak disorder leads to an intermediate symmetry-breaking condensation with Gamma-distributed disorder at the condensate site.

Findings

Existence of an intermediate condensation phase with Gamma-distributed disorder.

Identification of phases with normal and anomalous fluctuations.

Confirmation of a complex phase diagram as conjectured by prior work.

Abstract

Condensation phenomena in particle systems typically occur as one of two distinct types: either as a spontaneous symmetry breaking in a homogeneous system, in which particle interactions enforce condensation in a randomly located site, or as an explicit symmetry breaking in a system with background disorder, in which particles condensate in the site of extremal disorder. In this paper we confirm a recent conjecture by Godr\`eche and Luck by showing, for a zero range process with weak site disorder, that there exists a phase where condensation occurs with an intermediate type of symmetry-breaking, in which particles condensate in a site randomly chosen from a range of sites favoured by disorder. We show that this type of condensation is characterised by the occurrence of a Gamma distribution in the law of the disorder at the condensation site. We further investigate fluctuations of the condensate size and confirm a phase diagram, again conjectured by Godr\`eche and Luck, showing the existence of phases with normal and anomalous fluctuations.