Collapse in $1/r^α$ interacting systems

Details Collapse in $1/r^α$ interacting systems Collapse in $1/r^α$ interacting systems

2001-06-19

arxiv.org/abs/cond-mat/0106381v1

Physics

Condensed Matter

Statistical Mechanics

9 pages, 5 figures

Scientific paper

Collapse, or a gravitational-like phase transition is studied in a microcanonical ensemble of particles with an attractive $1/r^{\alpha}$ potential. A mean field continuous integral equation is used to determine a saddle-point density profile that extremizes the entropy functional. For all $0<\alpha<3$, a critical energy is determined below which the entropy of the system exhibits a discontinuous jump. If an effective short-range cutoff is applied, the entropy jump is finite; if not, the entropy diverges to $+\infty$. A stable integral equation solution represents a state with maximal entropy; the reverse is always true only for a modified integral equation introduced here.

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