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Large deviations for cluster size distributions in a continuous classical many-body system

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posted on 2023-06-09, 04:40 authored by Sabine Jansen, Wolfgang König, Bernd Metzger
An interesting problem in statistical physics is the condensation of classical particles in droplets or clusters when the pair-interaction is given by a stable Lennard–Jones-type potential. We study two aspects of this problem. We start by deriving a large deviations principle for the cluster size distribution for any inverse temperature ß?(0,8) ß?(0,8)and particle density ??(0,? cp ) ??(0,?cp)in the thermodynamic limit. Here ? cp >0 ?cp>0 is the close packing density. While in general the rate function is an abstract object, our second main result is the G G-convergence of the rate function toward an explicit limiting rate function in the low-temperature dilute limit ß?8 ß?8, ??0 ??0 such that -ß -1 log??? -ß-1log???? for some ??(0,8) ??(0,8). The limiting rate function and its minimisers appeared in recent work, where the temperature and the particle density were coupled with the particle number. In the decoupled limit considered here, we prove that just one cluster size is dominant, depending on the parameter ? ?. Under additional assumptions on the potential, the G G-convergence along curves can be strengthened to uniform bounds, valid in a low-temperature, low-density rectangle.

History

Publication status

  • Published

File Version

  • Published version

Journal

Annals of Applied Probability

ISSN

1050-5164

Publisher

Institute of Mathematical Statistics

Issue

2

Volume

25

Page range

930-973

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Probability and Statistics Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2017-01-16

First Open Access (FOA) Date

2017-01-16

First Compliant Deposit (FCD) Date

2017-01-16

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