Jönsson, Yoshino, and Nordblad Reply:

Abstract

Jönsson, Yoshino, and Nordblad Reply: In their Comment to our work [1], Berthier and Bouchaud [2] report results of temperature shifts T in a numerical simulation of a four-dimensional Edwards-Anderson Ising spin-glass model using the same thermal protocol as in [1]. Their scaling analysis yields an apparently similar result to ours.In our experiments the data are limited to a narrow temperature region jTj < 0:02 T g . The expected saturation of L eff to the overlap length L T [3] is not observed for these small values of jTj. In this Reply, we instead point out that our experimental results can be understood in terms of temperature chaos as partial rejuvenation in a weakly perturbed regime.Within the droplet theory [3], it is assumed that there are dangerously irrelevant droplets whose free-energy gaps F L are arbitrarily small. The gap can be smaller than dF with probability 0dF=L=L 0 , wherẽ 0 > 0. Consequently, a perturbation which amounts to a small free-energy gain of order UL=L 0 can induce a droplet excitation with a probability pL=L U 0L=L U . Here L U L 0 U= ÿ1= is the overlap length with the chaos exponent ÿ . In the case of T shifts, U k B jTj and d s =2, where d s is the surface fractal dimension of the droplets. Importantly, the probability pL=L U is nonzero in the weakly perturbed regime L < L U and increases with L if > 0 smoothly connecting to the strongly perturbedSupposing that L T > L T i t w , all length scales smaller than the domain size L T i t w belong to the weakly perturbed regime. A finite region of size L within a domain can then become out of equilibrium with the probability pL=L T . This reflects the breaking up of domains into smaller ones, yielding a broad distribution of domain sizes up to the maximum L max L T i t w . Then a simple scaling argument gives that the effective domain size surrounding an arbitrary point of the system on average reaches L eff L T FL max =L T with Fx x ÿ cx 1 . Here the second term in Fx, with c being a positive constant, yields a correction term, which is the first order of 0U= to the no-chaos limit of L eff . Higher order terms can be neglected for small enough jTj. It can be seen in Fig. 1 that the ansatz fits our data for jTj & 0:4 K.In the simulations of Berthier-Bouchaud [2], length scales L & 5 are probed while L T * 20. In [5] the spatial correlation function is found to decay to 0 only after L T i t w , being consistent with L max L T i t w . Then the rejuvenation found in [2] can be understood as partial rejuvenation due to the temperature chaos effect in a weakly perturbed regime. We note that emergence of the temperature chaos effect has been confirmed in the same model as in [2] with modest system sizes [6]. Indeed, we have found that the ansatz proposed above also fits the result of Berthier-Bouchaud [2] very well with c 0:15 and 1. However, the largest T shifts used in [2] involve temperatures in the range 0:8-0:9T g , within which numerical (but not experimental) length/ time scales are dominated by critical fluctuations as shown by Fig...

Rejuvenation and memory in model spin glasses in three and four dimensions

“…Experiments where ͑T 2 − T 1 ͒ / T 1 is very small can be accounted for by the cumulative aging scenario, 17,19 consisting in the three following hypotheses:…”

“…However, more complicated rules have been used. 5,[17][18][19] ͑ii͒ The coherence length always grows with time. It behaves continuously upon temperature changes.…”

“…Equation ͑4͒ is used in an indirect way, both in the analysis of simulations 9,27 and experiments. [17][18][19] Relations such as Eq. ͑3͒, obtained in a different experiment, are used to convert the measured effective times into length scales and vice versa.…”

“…Under very small temperature changes 17 ͓say ͑T 1 − T 2 ͒ / T 1 Ͻ 5 ϫ 10 −3 ͔ the behavior of the spin glass is rather smooth. On the other hand, sharp memory and rejuvenation can be observed 18 for ͑T 1 − T 2 ͒ / T 1 ϳ 0.07.…”

“…The crossover from small to drastic effects is rationalized using effective isothermal waiting times. 17,19 Consider the simplest temperature change protocol: a system is aged for time t w at temperature T 1 , then its temperature is suddenly shifted from T 1 to T 2 . After the shift, the ZFC magnetization is measured.…”