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Phase Transitions For Dilute Particle Systems with Lennard-Jones Potential

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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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Authors and Affiliations

  1. Dipartimento Matematica Applicata, Universita Ca’ Foscari, Venezia, Italy

    Andrea Collevecchio

  2. Weierstraß-Institut Berlin, Mohrenstr. 39, 10117, Berlin, Germany

    Wolfgang König

  3. Institut für Mathematik, Technische Universität Berlin, Str. des 17. Juni 136, 10623, Berlin, Germany

    Wolfgang König

  4. Department of Mathematical Sciences, University of Bath, Claverton Down, Bath, BA2 7AY, UK

    Peter Mörters

  5. Department of Mathematics, University College London, Gower Street, London, WC1 E6BT, UK

    Nadia Sidorova

Authors
  1. Andrea Collevecchio
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  2. Wolfgang König
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  3. Peter Mörters
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  4. Nadia Sidorova
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Corresponding author

Correspondence to Peter Mörters.

Additional information

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

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