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We rigorously characterize the KMS and the limiting Gibbs states for mean field models. As an application we prove the convergence of the Gibbs states for the Dicke Maser model in the infinite volume limit.

We consider the C*-algebras which contain the Weyl operators when the symplectic form which defines the C.C.R. is possibly degenerate. We prove that the C.C.R. are all obtained as a quotient of a universal C*-algebra by some of its ideals, and we characterize all these ideals.