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Large deviation principles and generalized Sherrington-Kirkpatrick models. (English) Zbl 1165.82311

Summary: We show how to prove large deviation principles for the overlaps of the usual Sherrington-Kirkpatrick model (at high enough temperature) by proving that some higher dimensional versions of this model are “solved by the replica-symmetric solution”. In the version where the spins are uniform over the sphere of radius \(\sqrt{d}\) of \(\mathbb R^d\), we prove that the critical temperature is bounded independently of \(d\).

MSC:

82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82D30 Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
60F10 Large deviations
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References:

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