An exactly solvable phase transition model: generalized statistics and generalized Bose-Einstein condensation

Details An exactly solvable phase transition model: generalized statistics and generalized Bose-Einstein condensation An exactly solvable phase transition model: generalized statistics and generalized Bose-Einstein condensation

2009-08-31

arxiv.org/abs/0908.4458v1

J. Stat. Mech. (2009) P07034

Physics

Condensed Matter

Statistical Mechanics

17 pages, 2 figures

Scientific paper

In this paper, we present an exactly solvable phase transition model in which the phase transition is purely statistically derived. The phase transition in this model is a generalized Bose-Einstein condensation. The exact expression of the thermodynamic quantity which can simultaneously describe both gas phase and condensed phase is solved with the help of the homogeneous Riemann-Hilbert problem, so one can judge whether there exists a phase transition and determine the phase transition point mathematically rigorously. A generalized statistics in which the maximum occupation numbers of different quantum states can take on different values is introduced, as a generalization of Bose-Einstein and Fermi-Dirac statistics.

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