Abstract
The equilibrium properties of classical self-gravitating systems in the grand canonical ensemble are studied by using the correspondence with an euclidean field theory with infrared and ultraviolet cutoffs. It is shown that the system develops a first order phase transition between a low and a high density regime. In addition, due to the long range of the gravitational potential, the system is close to criticality within each phase, with the exponents of mean field theory. The coexistence of a sharp first order transition and critical behavior can explain both the presence of voids in large regions of the universe as well as the self-similar density correlations in terms of self-gravity alone.
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