Abstract
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.
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Communicated by F. Toninelli
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Collevecchio, A., König, W., Mörters, P. et al. Phase Transitions For Dilute Particle Systems with Lennard-Jones Potential. Commun. Math. Phys. 299, 603–630 (2010). https://doi.org/10.1007/s00220-010-1097-5
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DOI: https://doi.org/10.1007/s00220-010-1097-5