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

Abstract

Some recent results concerning the Sherrington-Kirkpatrick model are reported. For $T$ near the critical temperature $T_c$, the replica free energy of the Sherrington-Kirkpatrick model is taken as the starting point of an expansion in powers of $\delta Q_{ab}=(Q_{ab}-Q_{ab}^{\mathrm{RS}})$ about the Replica Symmetric solution $Q_{ab}^{\mathrm{RS}}$. The expansion is kept up to 4-th order in $\delta \mathbf{Q}$ where a Parisi solution $Q_{ab}=Q(x)$ emerges, but only if one remains close enough to $T_c$. For $T$ near zero we show how to separate contributions from $x\ll T\ll 1$ where the Hessian maintains the standard structure of Parisi Replica Symmetry Breaking with bands of eigenvalues bounded below by zero modes. For $T\ll x\le 1$ 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 {\sl droplet-like} regime.

11 pages, 3 figures, Published version

References in corpus (8)

• Low temperature solution of the Sherrington-Kirkpatrick model
• Double Criticality of the Sherrington-Kirkpatrick Model at T=0
• Scaling and Renormalization Group in Replica Symmetry Breaking space: Evidence for a simple analytical solution of the SK model at zero temperature
• Sherrington-Kirkpatrick model near $T=T_c$: expanding around the Replica Symmetric Solution
• New technique for replica symmetry breaking with application to the SK-model at and near T=0
• Stability of the Parisi Solution for the Sherrington-Kirkpatrick model near T=0
• Low temperature spin glass fluctuations: expanding around a spherical approximation
• Low Temperature Mass Spectrum in the Ising Spin Glass

Cited by in corpus (1)

• Exact theory of dense amorphous hard spheres in high dimension. III. The full RSB solution