Growing length scales during aging in 2d disordered systems

TL;DR

This paper investigates the non-equilibrium aging dynamics in three 2D disordered models, revealing a temperature-dependent algebraic growth of a characteristic length scale during aging, with different interpretations across models.

Contribution

It demonstrates the existence of a growing length scale during aging in three distinct 2D disordered systems and characterizes its algebraic growth behavior.

Findings

Length scale grows algebraically with time in all models.

Growth exponent depends on temperature.

Different physical interpretations of the length scale in each model.

Abstract

The non-equilibrium dynamics of three paradigmatic models for two-dimensional systems with quenched disorder is studied with a focus on the existence and analysis of a growing length scale during aging at low temperatures: 1) The random bond Ising ferromagnet, 2) the Edwards-Anderson model for a spin glas, 3) the solid-on-solid model on a disordered substrate (equivalent to the sine-Gordon model with random phase shifts). Interestingly, we find in all three models a length scale that grows algebraically with time (up to the system size in cases 1 and 3, up to the finite equilibrium length in case 2) with a temperature dependent growth exponent. Whereas in cases 1 and 2 this length scale characterizes a coarsening process, it represents in case 3 the growing size of fluctuations during aging.