Phase transitions for dilute particle systems with Lennard-Jones potential

A Collevecchio, W Konig, Peter Morters, Nadia Sidorova

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We consider a classical dilute particle system in a large box with pair-interaction 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.
Original languageEnglish
Pages (from-to)603-630
Number of pages28
JournalCommunications in Mathematical Physics
Issue number3
Publication statusPublished - Nov 2010


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