Low Temperature Mass Spectrum in the Ising Spin Glass

Abstract

We study the spectrum of the Hessian of the Sherrington-Kirkpatrick model near T=0, whose eigenvalues are the masses of the bare propagators in the expansion around the mean-field solution. In the limit $T\ll 1$ two regions can be identified. The first for $x$ close to 0, where $x$ is the Parisi replica symmetry breaking scheme parameter. In this region the spectrum of the Hessian is not trivial, and maintains the structure of the full replica symmetry breaking state found at higher temperatures. In the second region $T\ll x\le 1$ as $T\to 0$, the bands typical of the full replica symmetry breaking state collapse and only two eigenvalues are found: a null one and a positive one. We argue that this region has a droplet-like behavior. In the limit $T\to 0$ the width of the full replica symmetry breaking region shrinks to zero and only the droplet-like scenario survives.

5 pages, 1 figure, EPL in press

References in corpus (8)

• Analysis of the infinity-replica symmetry breaking solution of the Sherrington-Kirkpatrick model
• Replica Fourier Transforms on Ultrametric Trees, and Block-Diagonalizing Multi-Replica Matrices
• Interface energies in Ising spin glasses
• Low temperature solution of the Sherrington-Kirkpatrick model
• Block diagonalizing ultrametric matrices
• Scaling and Renormalization Group in Replica Symmetry Breaking space: Evidence for a simple analytical solution of the SK model at zero temperature
• Universality class of replica symmetry breaking, scaling behavior, and the low-temperature fixed-point order function of the Sherrington-Kirkpatrick model
• On Equilibrium Dynamics of Spin-Glass Systems

Cited by in corpus (3)

• Stability of the Parisi Solution for the Sherrington-Kirkpatrick model near T=0
• Nature of spin glass order in physical dimensions
• The Sherrington-Kirkpatrick model near T_c and near T=0