Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2010-04-03
J. Stat. Phys. 140(5), 846-872 (2010)
Physics
Condensed Matter
Statistical Mechanics
30 pages, 8 figures; typos corrected, figures improved, added references
Scientific paper
10.1007/s10955-010-0017-6
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.
Chleboun Paul
Grosskinsky Stefan
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