Geometric and Probabilistic Aspects of Boson Lattice Models

  • Daniel Ueltschi
Part of the Progress in Probability book series (PRPR, volume 51)

Abstract

This review describes quantum systems of bosonic particles moving on a lattice. These models are relevant in statistical physics, and have natural ties with probability theory. The general setting is recalled and the main questions about phase transitions are addressed. A lattice model with Lennard-Jones potential is studied as an example of a system where first-order phase transitions occur.

A major interest of bosonic systems is the possibility of displaying a Bose-Einstein condensation. This is discussed in the light of the main existing rigorous result, namely its occurrence in the hard-core boson model. Finally, we consider another approach that involves the lengths of the cycles formed by the particles in the space-time representation; Bose-Einstein condensation should be related to positive probability of infinite cycles.

Keywords

Entropy Helium Stein Compressibility Incompressibility 

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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Daniel Ueltschi
    • 1
  1. 1.Department of PhysicsPrinceton UniversityPrinceton

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