Collapse in $1/r^α$ interacting systems

I. Ispolatov; E. G. D. Cohen

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arXiv · cond-mat/0106381

Collapse in $1/r^α$ interacting systems

I. Ispolatov·E. G. D. Cohen

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Abstract

Collapse, or a gravitational-like phase transition is studied in a microcanonical ensemble of particles with an attractive $1/r^α$ potential. A mean field continuous integral equation is used to determine a saddle-point density profile that extremizes the entropy functional. For all $0<α<3$, 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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I. Ispolatov, E. G. D. Cohen. 2001-06-19. Collapse in $1/r^α$ interacting systems. https://arxiv.org/abs/cond-mat/0106381

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