01-87 Daniel Ueltschi
Geometric and probabilistic aspects of boson lattice models (143K, LaTeX2e with 8 postscript figures) Mar 2, 01
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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.

Files: 01-87.src( 01-87.comments , 01-87.keywords , probo.tex , figcont.eps , figcyc1.eps , figcyc2.eps , figfeykac.eps , figgse.eps , figphd.eps , figpot.eps , figsptime.eps )