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 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
Cite
@article{arxiv.math-ph/0103002,
title = {Geometric and probabilistic aspects of boson lattice models},
author = {D. Ueltschi},
journal= {arXiv preprint arXiv:math-ph/0103002},
year = {2007}
}
Comments
22 pages, 8 figures