Numerical Study of Aging in the Generalized Random Energy Model

Abstract

Magnetizations are introduced to the Generalized Random Energy Model (GREM) and numerical simulations on ac susceptibility is made for direct comparison with experiments in glassy materials. Prominent dynamical natures of spin glasses, i.e., memory effect and reinitialization, are reproduced well in the GREM. The existence of many layers causing continuous transitions is very important for the two natures. Results of experiments in other glassy materials such as polymers, supercooled glycerol and orientational glasses, which are contrast to those in spin glasses, are interpreted well by the Single-layer Random Energy Model.KEYWORDS: aging, generalized random energy model, memory effect, reinitialization, temperature specific dynamics, cumulative dynamics §1. IntroductionIn spin glasses, it is well known that dynamical behavior strongly depends on history of the system after quenching from above the transition temperature T c . These phenomena are called aging and have been studied with various experimental protocols such as the isothermal, 1, 2) the T -shift 3, 4) and the T -cycle one. 5,6,7,8,9) From the theoretical point of view, aging phenomena have been studied along two different pictures, i.e., so-called droplet picture 10,11,12,13) and hierarchical picture. 5,7,8) The Generalized Random Energy Model (GREM) 14,15,16,17) is a model that belongs to the latter. This model has a hierarchical structure causing continuous transitions as the system is cooled down. These continuous transitions correspond to successive branching process of free energy in the hierarchical picture. Bouchaud and Dean 14) have shown that aging naturally occurs in this model and the time correlation function C(t + t w , t w ) satisfies a t/t w scaling law. Furthermore, we have recently made simulations 18,19) similar to experiments on aging phenomena with temperature variations. As the consequence, it has been shown that results of experiments are reproduced well according to the hierarchical picture.Recently, Jonason et al 20) have made a new experiment, in which curious dynamical natures of spin glasses are observed very clearly. This experiment consists of the following two runs. In the first run, the sample is continuously cooled from T max (> T c ) to T min (< T c ) at a constant rate, 1 and is immediately reheated at the same rate. During the cooling and the reheating, out-of-phase ac-susceptibility χ ′′ is measured as a function of temperature. We call this curve as χ ′′ ref .The difference between the observed value in the cooling and that in the reheating is not observed in spin glasses, while the hysteresis is observed in other glassy materials, such as polymer glasses, 21) orientational glasses 22) and disordered ferromagnets. 23) In the second run, the sample is cooled from T max to a waiting temperature T wait (T min < T wait < T c ), and is kept at T wait during a certain time interval. The sample ages and χ ′′ decreases during the interval. Then the system is cooled to T min and is reheated to T max without any stops. Her...

Neutrino Telescope Array (NTA) — Towards Survey of Astronomical ντ Sources

“…(1) number of detected photoelectrons per LC > 61; (2) S /N estimated in track-associated 4 × 64 pixel box (air-shower track included) > 4 [19]. A simulated event with primary ντ energy Eν τ = 10 eV, elevation angle −6.4 • and arrival direction towards Mauna Loa, consistent with the above conditions, is shown in Fig.…”

Spin Glasses: Experimental Signatures and Salient Outcomes

“…Details on the results in this regime of intermediate T values, together with their discussion in terms of a Random Energy Model, can be found in [67] (see also [69]). Many sets of temperature step experiments of this kind have been performed, by the Saclay group (see references in [45,44]) and also by the Uppsala group (see for example [70]), with similar results, even though sometimes discussed in slightly different terms.…”

Deviations from perfect memory in spin glass temperature cycling experiments

“…These models have been shown [14,15,16,17,18,19] to reproduce many of the experimental features of aging, including rejuvenation and memory. We find that the non monotonous transients mentioned above can also be obtained in such models.…”