On the out of equilibrium order parameters in long-range spin-glases

TL;DR

This paper investigates the out-of-equilibrium dynamics of long-range spin glasses, revealing self-similar landscape structures and connections between dynamical and equilibrium states through distribution analysis of auto-correlation functions.

Contribution

It introduces a novel way to express dynamical order parameters via distributions of auto-correlation and response functions, linking out-of-equilibrium and equilibrium landscapes.

Findings

Distributions of auto-correlation functions are calculated for the SK model at long times.

The out-of-equilibrium landscape exhibits self-similarity over different times.

A formal connection between dynamical and replica approaches is highlighted.

Abstract

We show that the dynamical order parameters can be reexpressed in terms of the distribution of the staggered auto-correlation and response functions. We calculate these distributions for the out of equilibrium dynamics of the Sherrington-Kirpatrick model at long times. The results suggest that the landscape this model visits at different long times in an out of equilibrium relaxation process is, in a sense, self-similar. Furthermore, there is a similarity between the landscape seen out of equilibrium at long times and the equilibrium landscape. The calculation is greatly simplified by making use of the superspace notation in the dynamical approach. This notation also highlights the rather mysterious formal connection between the dynamical and replica approaches.