Domain growth and aging scaling in coarsening disordered systems

Abstract

Abstract. Using extensive Monte Carlo simulations we study aging properties of two disordered systems quenched below their critical point, namely the two-dimensional random-bond Ising model and the threedimensional Edwards-Anderson Ising spin glass with a bimodal distribution of the coupling constants. We study the two-times autocorrelation and space-time correlation functions and show that in both systems a simple aging scenario prevails in terms of the scaling variable L(t)/L(s), where L is the time-dependent correlation length, whereas s is the waiting time and t is the observation time. The investigation of the space-time correlation function for the random-bond Ising model allows us to address some issues related to superuniversality.

Aging processes in systems with anomalous slow dynamics

“…In cases with an algebraic growth law L(t) ∼ t 1/z , as observed in critical systems or coarsening systems without disorder, one usually uses t/s as the scaling variable. However, for more complicated cases with subleading contributions to the growth and/or crossover between an initial algebraic growth and the true asymptotic behavior, this approach is too simplistic and L(t)/L(s) has to be used as variable in order to achieve the expected scaling [11,15].…”

“…Whereas in some of the studies on disordered Ising models aging phenomena in the crossover regime were investigated [10][11][12][13][14][15], none of these recent numerical studies was able to enter so deeply into the asymptotic regime that no corrections to the logarithmic growth law were detectable anymore. Therefore a systematic study of aging processes in this regime with pure logarithmic growth has not yet been done.…”

Physical Aging of Classical Oscillators

“…In common to all of these systems are ultraslow relaxations that are characteristically different from relaxation in ordered systems, as they involve a very broad distribution of relaxation times and effective activation energies. So the associated energy landscape is rough as a result of randomness and/or frustration, and ergodicity is weakly broken [8].Another set of systems, in which aging is observed, shares a different kind of slow processes, which are related to growth [9,10], coarsening [11], diffusion, and subdiffusion [12,13], leading to a critical slowing of the dynamics, often with a similar type of dynamical scaling as in the first set of models. Aging in a Hamiltonian system of coupled rotators was also observed for conservative dynamics, remarkably without a thermal bath and without disorder or frustration [14], but for a particular family of initial conditions in the specific limits of infinite-range couplings, and the thermodynamic limit N → ∞ taken before the large time limit t → ∞.…”

“…Another set of systems, in which aging is observed, shares a different kind of slow processes, which are related to growth [9,10], coarsening [11], diffusion, and subdiffusion [12,13], leading to a critical slowing of the dynamics, often with a similar type of dynamical scaling as in the first set of models. Aging in a Hamiltonian system of coupled rotators was also observed for conservative dynamics, remarkably without a thermal bath and without disorder or frustration [14], but for a particular family of initial conditions in the specific limits of infinite-range couplings, and the thermodynamic limit N → ∞ taken before the large time limit t → ∞.…”

“…This scaling ansatz is chosen in analogy to an ansatz used in spin glasses, for example, in the three-dimensional EdwardsAnderson Ising spin glass [11], and corresponds to socalled simple aging. In Fig.…”