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A mathematical reformulation of Derrida’s REM and GREM. (English) Zbl 0617.60100

The author investigates two statistical models introduced by B. Derrida and called respectively random energy model (REM) [Random-energy model: Limit of a family of disordered models, Phys. Rev. Lett. 45, 79-82 (1982), and Random-energy model: An exactly solvable model of disordered systems, Phys. Rev. B 24, 2613-2626 (1981)] and general random energy model (GREM) [A generalization of the random energy model which includes correlations between energies, J. Phys. Lett. 46, L401-L407 (1985), and B. Derrida and E. Gardner, Solution of the generalized random energy model, J. Phys. C, in press (1986)].
In Derrida’s original formulation of the REM and GREM certain limits are implicit. By means of a modification of the Poisson distribution on the corresponding configurational space the author gives a mathematical reformulation where these limits have already been taken. It permits for instance to perform more systematic calculations of relevance to Parisi’s solution of the Sherrington-Kirkpatrick spin-glass model.
Reviewer: S.Pogosian

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
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References:

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