Thermodynamics of the self-gravitating ring model

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We present the phase diagram, in both the microcanonical and the canonical ensemble, of the selfgravitating-ring sSGRd model, which describes the motion of equal point masses constrained on a ring andsubject to 3D gravitational attraction. If the interaction is regularized at short distances by the introduction ofa softening parameter, a global entropy maximum always exists, and thermodynamics is well defined in themean-field limit. However, ensembles are not equivalent and a phase of negative specific heat in the microcanonicalensemble appears in a wide intermediate energy region, if the softening parameter is small enough.The phase transition changes from second to first order at a tricritical point, whose location is not the same inthe two ensembles. All these features make of the SGR model the best prototype of a self-gravitating systemin one dimension. In order to obtain the stable stationary mass distribution, we apply an iterative method,inspired by a previous one used in 2D turbulence, which ensures entropy increase and, hence, convergence towards an equilibrium state.
2005-05-00