METASTATES IN DISORDERED MEAN-FIELD MODELS II - THE SUPERSTATES

We continue to investigate the size dependence of disordered mean-fiel d models with finite local spin space in more detail, illustrating the concept of ''superstates'' as recently proposed by Bovier and Gayrard . We discuss various notions of convergence for the behavior of the pa ths (t --> mu([tN])(eta))(t is an element of (0, 1]) in the thermodyna mic limit N up arrow) infinity. Here mu(n)(eta) is the Gibbs measure i n the finite volume {1,..., n} and eta is the disorder variable. In pa rticular we prove refined convergence statements in our concrete examp les, the Hopfield model with finitely many patterns (having continuous paths) and the Curie-Weiss random-field Ising model (having singular paths).