Aging processes in systems with anomalous slow dynamics

TL;DR

This paper investigates aging and dynamical scaling in systems with anomalously slow, logarithmic domain growth, using simple models to understand the underlying relaxation processes and their broader implications.

Contribution

It introduces a detailed analysis of aging in systems with slow, logarithmic growth, providing a simple scaling framework applicable to disordered ferromagnets and spin glasses.

Findings

A simple aging picture emerges during logarithmic growth.

Two-times correlation and response functions reveal aging dynamics.

Scaling with the growth length captures the slow relaxation behavior.

Abstract

Recently, different numerical studies of coarsening in disordered systems have shown the existence of a crossover from an initial, transient, power-law domain growth to a slower, presumably logarithmic, growth. However, due to the very slow dynamics and the long lasting transient regime, one is usually not able to fully enter the asymptotic regime when investigating the relaxation of these systems toward equilibrium. We here study two simple driven systems, the one-dimensional $ABC$ model and a related domain model with simplified dynamics, that are known to exhibit anomalous slow relaxation where the asymptotic logarithmic growth regime is readily accessible. Studying two-times correlation and response functions, we focus on aging processes and dynamical scaling during logarithmic growth. Using the time-dependent growth length as the scaling variable, a simple aging picture emerges that is expected to also prevail in the asymptotic regime of disordered ferromagnets and spin glasses.