Phase transitions in systems with 1/r(alpha) attractive interactions.
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 +infinity. A stable integral equation solution represents a state with maximal entropy; the reverse is always true only for a modified integral equation introduced here.
Ispolatov
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I
Center for Studies in Physics and Biology, Rockefeller University, New York, New York 10021, USA.
Cohen
E G
EG