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We discuss the nature of phase transitions in self-gravitating systems bothin the microcanonical and in the canonical ensemble. We avoid the divergence ofthe gravitational potential at short distances by considering the case ofself-gravitating fermions and hard spheres models. Three kinds of phasetransitions (of zeroth, first and second order) are evidenced. They separate a``gaseous'' phase with a smoothly varying distribution of matter from a``condensed'' phase with a core-halo structure. We propose a simple analyticalmodel to describe these phase transitions. We determine the value of energy (inthe microcanonical ensemble) and temperature (in the canonical ensemble) at thetransition point and we study their dependance with the degeneracy parameter(for fermions) or with the size of the particles (for a hard spheres gas).Scaling laws are obtained analytically in the asymptotic limit of a small shortdistance cut-off. Our analytical model captures the essential physics of theproblem and compares remarkably well with the full numerical solutions.Comment: Submitted to Phys. Rev. E. New material adde

Phase transitions in self-gravitating systems: Self-gravitating fermions and hard-sphere models