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PHASE TRANSITIONS FOR DILUTE PARTICLE SYSTEMS WITH LENNARD-JONES POTENTIAL

By Andrea Collevecchio, Wolfgang König, Peter Mörters and Nadia Sidorova

Abstract

Abstract: We consider a classical dilute particle system in a large box with pairinteraction given by a Lennard-Jones-type potential. The inverse temperature is picked proportionally to the logarithm of the particle density. We identify the free energy per particle in terms of a variational formula and show that this formula exhibits a cascade of phase transitions as the temperature parameter ranges from zero to infinity. Loosely speaking, the particle system separates into spatially distant components in such a way that within each phase all components are of the same size, which is the larger the lower the temperature. The main tool in our proof is a new large deviation principle for sparse point configurations

Topics: Lennard-Jones-type potential, dilute system, large deviations
Year: 2010
OAI identifier: oai:CiteSeerX.psu:10.1.1.190.4995
Provided by: CiteSeerX
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