Phase transitions in systems with 1/r(alpha) attractive interactions - art. no. 056103

Collapse, or a gravitational-like phase transition is studied in a microcan onical ensemble of particles with an attractive l/r(alpha) potential. A mea n-field continuous integral equation is used to determine a saddle-point de nsity profile that extremizes the entropy functional. For all 0<<alpha><3, a critical energy is determined below which the entropy of the system exhib its a discontinuous jump. If an effective short-range cutoff is applied, th e entropy jump is finite; if not, the entropy diverges to + <infinity>. A s table integral equation solution represents a state with maximal entropy; t he reverse is always true only for a modified integral equation introduced here.