Classification of phase transitions and ensemble inequivalence, in systems with long range interactions

Details Classification of phase transitions and ensemble inequivalence, in systems with long range interactions Classification of phase transitions and ensemble inequivalence, in systems with long range interactions

2003-03-17

arxiv.org/abs/cond-mat/0303307v2

J.Statist.Phys. 118 (2005) 1073-1105

Physics

Condensed Matter

Statistical Mechanics

42 pages, 11 figures. Accepted in Journal of Statistical Physics. Final version

Scientific paper

Systems with long range interactions in general are not additive, which can lead to an inequivalence of the microcanonical and canonical ensembles. The microcanonical ensemble may show richer behavior than the canonical one, including negative specific heats and other non-common behaviors. We propose a classification of microcanonical phase transitions, of their link to canonical ones, and of the possible situations of ensemble inequivalence. We discuss previously observed phase transitions and inequivalence in self-gravitating, two-dimensional fluid dynamics and non-neutral plasmas. We note a number of generic situations that have not yet been observed in such systems.

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