Journal of Statistical Physics

, Volume 140, Issue 5, pp 846–872 | Cite as

Finite Size Effects and Metastability in Zero-Range Condensation

  • Paul ChlebounEmail author
  • Stefan Grosskinsky


We study zero-range processes which are known to exhibit a condensation transition, where above a critical density a non-zero fraction of all particles accumulates on a single lattice site. This phenomenon has been a subject of recent research interest and is well understood in the thermodynamic limit. The system shows large finite size effects, and we observe a switching between metastable fluid and condensed phases close to the critical point, in contrast to the continuous limiting behaviour of relevant observables. We describe the leading order finite size effects and establish a discontinuity near criticality in a rigorous scaling limit. We also characterise the metastable phases using a current matching argument and an extension of the fluid phase to supercritical densities. This constitutes an interesting example where the thermodynamic limit fails to capture essential parts of the dynamics, which are particularly relevant in applications with moderate system sizes such as traffic flow or granular clustering.


Zero range process Condensation Metastability Finite size effects Large deviations 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Mathematics Institute and Centre for Complexity ScienceUniversity of WarwickCoventryUK

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