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Metastates in disordered mean-field models II: The superstates

Kulske, C., Apr-1998, In : Journal of Statistical Physics. 91, 1-2, p. 155-176 22 p.

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  • Journal of Statistical Physics, Vol. 91, Nos. 1/2, 1998Metastates in Disordered Mean-Field Models II:The Superstates

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DOI

  • C Kulske

We continue to investigate the size dependence of disordered mean-field 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 paths (t --> mu([tN])(eta))(t is an element of (0, 1]) in the thermodynamic limit N up arrow) infinity. Here mu(n)(eta) is the Gibbs measure in the finite volume {1,..., n} and eta is the disorder variable. In particular we prove refined convergence statements in our concrete examples, the Hopfield model with finitely many patterns (having continuous paths) and the Curie-Weiss random-field Ising model (having singular paths).

Original languageEnglish
Pages (from-to)155-176
Number of pages22
JournalJournal of Statistical Physics
Volume91
Issue number1-2
Publication statusPublished - Apr-1998

    Keywords

  • disordered systems, size dependence, random Gibbs states, metastates, superstates, mean-field models, Hopfield model random field model, SYSTEMS

ID: 121200517