Nonequilibrium dynamics below the super-roughening transition

The nonequilibrium relaxational dynamics of the solid-on-solid model on a disordered substrate and the sine-Gordon model with random phase shifts is studied numerically. Close to the super-roughening temperature Tg our results for the autocorrelations, spatial correlations, and response function as well as for the fluctuation dissipation ratio agree well with the prediction of a recent one-loop renormalization-group sRGd calculation, whereas deep in the glassy low-temperature phase substantial deviations occur. The change in the lowtemperature behavior of these quantities compared to the RG predictions is shown to be contained in a change of the functional temperature dependence of the dynamical exponent zsTd, which relates the age t of the system to a length scale Lstd :zsTd changes from a linear T dependence close to Tg to a 1/T behavior far away from Tg. By identifying spatial domains as connected patches of the exactly computable ground states of the system we demonstrate that the growing length scale Lstd is the characteristic size of thermally fluctuating clusters around “typical” long-lived configurations.