Geometric and probabilistic aspects of boson lattice models
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 LennardJones potential is studied as an example of a system where firstorder phase transitions occur. A major interest of bosonic systems is the possibility of displaying a BoseEinstein condensation. This is discussed in the light of the main existing rigorous result, namely its occurrence in the hardcore boson model. Finally, we consider another approach that involves the lengths of the cycles formed by the particles in the spacetime representation; BoseEinstein condensation should be related to positive probability of infinite cycles.
 Publication:

arXiv eprints
 Pub Date:
 March 2001
 arXiv:
 arXiv:mathph/0103002
 Bibcode:
 2001math.ph...3002U
 Keywords:

 Mathematical Physics;
 82B10;
 82B20;
 82B26;
 82B41;
 60K40
 EPrint:
 22 pages, 8 figures