Extracting the Landscape and Morphology of Aging Glassy Systems

TL;DR

This paper introduces a method to analyze the energy landscape of aging glassy systems using time series data, linking non-equilibrium events to record statistics, and studying aging in Ising spin glasses.

Contribution

It presents a novel approach to characterize landscape geometry and aging dynamics in glassy systems based solely on energy time series analysis.

Findings

Energy barriers scale with temperature and system size.

Lowest energies in valleys scale with system size.

Relaxation behavior follows a $\, ext{ln}\, t$ pattern.

Abstract

We propose a way to analyze the landscape geometry explored by a glassy system after a quench solely based on time series of energy values recorded during a simulation. Entry and exit times for landscape `valleys' are defined operationally by the occurrence of anomalous energy changes revealed by barrier and energy records. Linking these non-equilibrium events--or `earthquakes'-- to the record statistics of the thermal noise immediately leads to the $\ln t$ relaxation behavior ubiquitous in glassy dynamics. Aging of Ising spin glasses in two and three dimensions is studied as a check for a number of low temperatures and lattice sizes. A simple picture emerges on e.g. 1) the scaling with temperature and system size of the energy barriers as function of the valley index, and 2) the scaling with system size of the lowest energy seen in each valley.