Abstract
Collapse, or a gravitational-like phase transition, is found in microcanonical ensembles of particles with an attractive 1/r(alpha) potential not only for alpha = 1 but for all 0<alpha<3. The phase behavior of the system is complex: If an effective sufficiently short-range cutoff is applied, the density of the collapsed phase is finite everywhere; if not, the collapse results in a density singularity. Also, with increasing effective cutoff range, the gravitational phase transition will cross over to a normal first-order phase transition.
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