Non equilibrium dynamics below the super-roughening transition

TL;DR

This paper investigates the non-equilibrium relaxation dynamics of disordered models near and below the super-roughening transition, revealing temperature-dependent dynamical exponents and domain growth behaviors through numerical simulations.

Contribution

It provides a detailed numerical study of non-equilibrium dynamics in disordered surface models, confirming RG predictions near the transition and identifying deviations at low temperatures.

Findings

Agreement with RG predictions near $T_g$ for autocorrelations and FDR

Deviation from RG predictions at low temperatures

The dynamical exponent $z(T)$ changes from linear to 1/T behavior away from $T_g$

Abstract

The non equilibrium 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 $T_g$ our results for the autocorrelations, spatial correlations and response function as well as for the fluctuation dissipation ratio (FDR) agree well with the prediction of a recent one loop RG calculation, whereas deep in the glassy low temperature phase substantial deviations occur. The change in the low temperature behavior of these quantities compared with the RG predictions is shown to be contained in a change of the functional temperature dependence of the dynamical exponent $z(T)$, which relates the age $t$ of the system with a length scale ${\cal L}(t)$: $z(T)$ changes from a linear $T$-dependence close to $T_g$ to a 1/T-behavior far away from $T_g$. By identifying spatial domains as connected patches of the exactly computable ground states of the system we demonstrate that the growing length scale ${\cal L}(t)$ is the characteristic size of thermally fluctuating clusters around ``typical'' long-lived configurations.