The Sherrington-Kirkpatrick model near <i>T<sub>c</sub></i> and near <i>T=0</i> - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Philosophical Magazine Année : 2011

The Sherrington-Kirkpatrick model near Tc and near T=0

Résumé

Some recent results concerning the Sherrington-Kirkpatrick model are reported. For T near the critical temperature Tc, the replica free energy of the Sherrington-Kirkpatrick model is taken as the starting point of an expansion in powers of δQab = (Qab - QabRS) about the Replica Symmetric solution QabRS. The expansion is kept up to 4-th order in δQ where a Parisi solution Qab = Q(x) emerges, but only if one remains close enough to Tc. For T near zero we show how to separate contributions from x " T " 1 where the Hessian maintains the standard structure of Parisi Replica Symmetry Breaking with bands of eigenvalues bounded below by zero modes. For T " x ≤ 1 the bands collapse and only two eigenvalues, a null one and a positive one, are found. In this region the solution stands in what can be called a droplet-like regime.

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Dates et versions

hal-00747308 , version 1 (31-10-2012)

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Andrea Crisanti, Cirano de Dominicis. The Sherrington-Kirkpatrick model near Tc and near T=0. Philosophical Magazine, 2011, pp.1. ⟨10.1080/14786435.2011.611120⟩. ⟨hal-00747308⟩
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