### Reference:

Collevecchio, A., Konig, W., Morters, P. and Sidorova, N., 2010. Phase transitions for dilute particle systems with Lennard-Jones potential. *Communications in Mathematical Physics*, 299 (3), pp. 603-630.

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### Official URL:

http://dx.doi.org/10.1007/s00220-010-1097-5

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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.

Item Type | Articles |

Creators | Collevecchio, A., Konig, W., Morters, P. and Sidorova, N. |

DOI | 10.1007/s00220-010-1097-5 |

Related URLs | |

Departments | Faculty of Science > Mathematical Sciences |

Research Centres | |

Publisher Statement | Morters_CommMathPhy_2010_299_3_603.pdf: The original publication is available at www.springerlink.com |

Refereed | Yes |

Status | Published |

ID Code | 16680 |

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