Multiple domain growth and memory in the droplet model for spin-glasses

Abstract

We study domain growth dynamics when the target state is suddenly changed on all length scales. This procedure mimics the 'chaos' effect postulated by the droplet theory of spin-glasses, and allows us to investigate in details its various dynamical consequences. We study the problem by a variety of methods, including scaling arguments, analytical solution of the spherical Mattis model, and Monte Carlo simulations of a 2-dimensional Ising Mattis model. We show that successive coarsening with respect to different equilibrium states imprints multiple domain structures on top of each other, plus extra noise due to random interferences. We demonstrate that the domain structures can be retrieved by an additional series of coarsening in the reversed order which removes the noises. We discuss the rejuvenation (chaos) and memory effects observed in temperature-cycling experiments in glassy systems from the present point of view, and discuss some open problems and alternative descriptions.

Spin glasses: model systems for non-equilibrium dynamics

“…One recent theoretical development of the droplet model introducing the ghost domain concept [16] provides a visual illustration of how an original domain structure is recovered after a perturbation that intuitively should destroy any memory of the preceding aging process. The procedure and process are illustrated in figure 5 for bond perturbations on a 2d Mattis model.…”

“…However, at this temperature, a (ghost) pattern of the original domain structure remains and the Figure 5. The evolution of domains in a 2d Mattis model [16] during a bond perturbation experiment. The system is allowed to evolve under two different interaction patterns having completely different ground states (A and B).…”

Aging behavior of spin glasses under bond and temperature perturbations from laser illumination

“…Recently, aging behavior under the bond or temperature cycle has been explained based on the behavior of domains in terms of the ghost domain picture. 10,11,12 In the following paragraphs, we interpret our results based on the behavior of the domain under the bond or temperature cycle in the same way. We divide our experimental protocol into three stages according to Fig.…”

“…These contradictory aspects can be explained based on the ghost domain scenario. 7,10,11,12 Thus, the crossover between a weakly perturbed regime (L < L ∆X ) and a strongly perturbed regime (L < L ∆X ) 11,12 should be clarified so that we can gain an intrinsic understanding of the rejuvenation and memory effects based on the droplet picture.…”

“…In such an experimental protocol based on temperature change, however, this change inevitably affects the thermal excitation of the droplet and thus leads to strong separation of the time scales. 10 This makes it difficult to demonstrate the existence temperature chaos. In fact, several papers 18,19,20,21 claim that the rejuvenationmemory effects observed in temperature cycling can be attributed to the differences among the length scales caused by the change in temperature.…”