Collapse in 1/rα interacting systems
Ispolatov, I. · Cohen, E. G. D.
Original · EN
Collapse, or a gravitational-like phase transition is studied in a microcanonical ensemble of particles with an attractive 1/rα 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 +∞. 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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