title: Phase transitions in systems with 1/r(alpha) attractive interactions.
abstract: 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.
authors.affiliation: Center for Studies in Physics and Biology, Rockefeller University, New York, New York 10021, USA.
authors.forename: I
authors.initials: I
authors.lastname: Ispolatov
authors.forename: E G
authors.initials: EG
authors.lastname: Cohen