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Systems with long-range interactions, such as self-gravitating clusters andmagnetically confined plasmas, do not relax to the usual Boltzmann-Gibbsthermodynamic equilibrium, but become trapped in quasi-stationary states (QSS)the life time of which diverges with the number of particles. The QSS arecharacterized by the lack of ergodicity which can result in a symmetry brokenQSS starting from a spherically symmetric particle distribution. We willpresent a theory which allows us to quantitatively predict the instabilitythreshold for spontaneous symmetry breaking for a class of d-dimensionalself-gravitating systems.

Symmetry Breaking in d-Dimensional Self-gravitating Systems