Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2010-03-09
J. Stat. Mech. (2010) P05006
Physics
Condensed Matter
Statistical Mechanics
21 pages, 6 figures; submitted to JSTAT for the special issue on long-range interactions
Scientific paper
10.1088/1742-5468/2010/05/P05006
We introduce and discuss an effective model of a self-gravitating system whose equilibrium thermodynamics can be solved in both the microcanonical and the canonical ensemble, up to a maximization with respect to a single variable. Such a model can be derived from a model of self-gravitating particles confined on a ring, referred to as the self-gravitating ring (SGR) model, allowing a quantitative comparison between the thermodynamics of the two models. Despite the rather crude approximations involved in its derivation, the effective model compares quite well with the SGR model. Moreover, we discuss the relation between the effective model presented here and another model introduced by Thirring forty years ago. The two models are very similar and can be considered as examples of a class of minimal models of self-gravitating systems.
Casetti Lapo
Nardini Cesare
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