Growing correlations and aging of an elastic line in a random potential

Abstract

We study the thermally assisted relaxation of a directed elastic line in a two dimensional quenched random potential by solving numerically the Edwards-Wilkinson equation and the Monte Carlo dynamics of a solid-on-solid lattice model. We show that the aging dynamics is governed by a growing correlation length displaying two regimes: an initial thermally dominated power-law growth which crosses over, at a static temperature-dependent correlation length $L_T \sim T^3$, to a logarithmic growth consistent with an algebraic growth of barriers. We present a scaling arguments to deal with the crossover-induced geometrical and dynamical effects. This analysis allows to explain why the results of most numerical studies so far have been described with effective power-laws and also permits to determine the observed anomalous temperature-dependence of the characteristic growth exponents. We argue that a similar mechanism should be at work in other disordered systems. We generalize the Family-Vicsek stationary scaling law to describe the roughness by incorporating the waiting-time dependence or age of the initial configuration. The analysis of the two-time linear response and correlation functions shows that a well-defined effective temperature exists in the power-law regime. Finally, we discuss the relevance of our results for the slow dynamics of vortex glasses in High-Tc superconductors.Comment: 18 pages, 15 figures, submitted for publicatio

Aging in coarsening diluted ferromagnets

“…18 This is expected to be different in disordered systems as here a crossover from a transient, preasymptotic, power-law regime to an asymptotic regime with a slower, logarithmic, growth is predicted to happen. 20 There is mounting evidence, due to recent studies of elastic lines in disordered media, [7][8][9] that this crossover indeed takes place. Obviously, this crossover has to be taken into account in order to elucidate the scaling properties of disordered systems relaxing toward equilibrium.…”

“…New insights into this matter have come very recently through a series of papers on the dynamics of elastic lines in a random potential. [7][8][9] These papers provide convincing evidence for a dynamic crossover between a transient regime, characterized by a power-law growth with an effective dynamical exponent that depends on the disorder, and the asymptotic regime where the growth is logarithmic in time. This result strongly suggests the possibility that a similar crossover could take place in disordered ferromagnets and that the observed power-law regime with nonuniversal dynamical exponents is not the asymptotic regime.…”

“…One issue that has attracted much attention recently concerns ordering processes, relaxation phenomena, and the formation of domains in disordered systems. Examples include vortex lines in disordered type-II superconductors, [1][2][3][4][5] polymers in random media, [6][7][8][9] coarsening of disordered magnets, [10][11][12][13][14][15] and slow dynamics in spin glasses. 13,16,17 Our understanding of relaxation phenomena and aging processes in nonfrustrated systems with slow dynamics has greatly progressed during the last decade, mainly through the systematic study of critical and coarsening ferromagnets ͑see Ref.…”

Nanoscale studies of ferroelectric domain walls as pinned elastic interfaces

“…An especially interesting realisation of such out-of-equilibrium phenomena is provided by quenches, in which a parameter such as temperature or the appropriate conjugate field is abruptly varied. Numerical studies of interfaces subjected to quenches [163,164,165,166,167] have shown ageing of the interface and a longterm memory of the initial configuration. For ferroelectrics, Likodimos et al [95,103] studied domain evolution in cleaved triglycine sulfate crystals ( Fig.…”

Phenomenology of aging in the Kardar-Parisi-Zhang equation

“…In order to define a response, we appeal to the procedures used in irreversible systems [15,17,18,31] where the external field is related to a local change of rates. In the KK model, we consider a space-dependent deposition rate p i = p 0 + a i ε/2 with a i = ±1 and ε = 0.005 a small parameter.…”