On the Out of Equilibrium Relaxation of the Sherrington - Kirkpatrick model

TL;DR

This paper analytically investigates the long-time out-of-equilibrium relaxation behavior of the Sherrington-Kirkpatrick spin-glass model, revealing persistent non-equilibrium states and introducing triangle relations as a new analytical tool.

Contribution

It provides the first analytical description of the large-time out-of-equilibrium dynamics of the SK model, utilizing triangle relations to analyze the system's geometry over time.

Findings

System remains out of equilibrium indefinitely.

Triangle relations effectively describe configuration geometry.

Analytical results match numerical simulations.

Abstract

We derive analytical results for the large-time relaxation of the Sherrington - Kirkpatrick model in the thermodynamic limit, starting from a random configuration. The system never achieves local equilibrium in any fixed sector of phase-space, but remains in an asymptotic out of equilibrium regime. We propose as a tool, both numerical and analytical, for the study of the out of equilibrium dynamics of spin-glass models the use of `triangle relations' which describe the geometry of the configurations at three (long) different times.