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.
Domaines
Matière Condensée [cond-mat]
Origine : Fichiers produits par l'(les) auteur(s)
Loading...