Growing Length Scales during Aging in 2d Disordered Systems

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 glass, 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.