Phase Transitions in Systems with 1/r ^α Attractive Interactions

Abstract

We study the gravitational collapse — like phase transitions in the microcanonical ensemble for a class of systems of N particles with nonintegrable attractive pair potentials 1/r ^α, with 0 < α < 3 in three dimensions. Introducing a continuum description and a mean field approximation in the limit N to infinity, an integral equation for the density profile of the particles is obtained, which is solved numerically. For all 0 < α < 3 and sufficiently small short range cutoffs r ₀, there appears to be cutoff-independent critical energy, below which the system jumps discontinuously from a normal uniform to a collapsed core — halo state. This gravitational-like transition will become a normal first order transition when the cutoff range r ₀ becomes larger than some critical value r _0c which is an increasing function of α.