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arXiv:cond-mat/0205276 · Journal of the Physical Society of Japan

Numerical Study on Aging Dynamics in the 3D Ising Spin–Glass Model: III. Cumulative Memory and `Chaos' Effects in the Temperature-Shift Protocol

Hajime Takayama, Koji Hukushima

Published Dec 15, 2002• 27 citations
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Abstract

The temperature ($T$)-shift protcol of aging in the 3 dimensional (3D) Edwards- Anderson (EA) spin-glass (SG) model is studied through the out-of-phase component of the ac susceptibility simulated by the Monte Carlo method. For processes with a small magnitude of the $T$-shift, $ΔT$, the memory imprinted before the $T$-shift is preserved under the $T$-change and the SG short-range order continuously grows after the $T$-shift, which we call the cumulative memory scenario. For a negative $T$-shift process with a large $ΔT$ the deviation from the cumulative memory scenario has been observed for the first time in the numerical simulation. We attribute the phenomenon to the `chaos effect' which, we argue, is qualitatively different from the so-called rejuvenation effect observed just after the $T$-shift.

DOI
10.1143/jpsj.71.3003

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The temperature (TTT)-shift protcol of aging in the 3 dimensional (3D) Edwards- Anderson (EA) spin-glass (SG) model is studied through the out-of-phase component of the ac susceptibility simulated by the Monte Carlo method. For processes with a small magnitude of the TTT-shift, ΔTΔTΔT, the memory imprinted before the TTT-shift is preserved under the TTT-change and the SG short-range order continuously grows after the TTT-shift, which we call the cumulative memory scenario. For a negative TTT-shift process with a large ΔTΔTΔT the deviation from the cumulative memory scenario has been observed for the first time in the numerical simulation. We attribute the phenomenon to the `chaos effect' which, we argue, is qualitatively different from the so-called rejuvenation effect observed just after the TTT-shift.
Spin-glass (SG) states of the 3-dimensional Ising Edwards-Anderson model under a static magnetic field hhh are examined by means of the standard Monte Carlo simulation on the field-shift aging protocol at temperature TTT. For each process with $(T; \tw, h)$, $\tw$ being the waiting time before the field is switched on, we extract the dynamical crossover time, $\tcr(T; \tw, h)$. We have found a nice scaling relation between the two characteristic length scales which are properly determined from $\tcr$ and $\tw$ and then are normalized by the static field crossover length introduced in the SG droplet theory. This scaling behavior implies the instability of the SG phase in the equilibrium limit even under an infinitesimal hhh. In comparison with this numerical result the field effect on real spin glasses is also discussed.
We numerically study aging for the Edwards-Anderson model in three and four dimensions using different temperature-change protocols. In D=3D=3D=3, time scales a thousand times larger than in previous work are reached with the Spin Update Engine (SUE) machine. Deviations from cumulative aging are observed in the nonmonotonic time behavior of the coherence length. Memory and rejuvenation effects are found in a temperature-cycle protocol, revealed by vanishing effective waiting times. Similar effects are reported for the D=3D=3D=3 site-diluted ferromagnetic Ising model (without chaos). However, rejuvenation is reduced if off-equilibrium corrections to the fluctuation-dissipation theorem are considered. Memory and rejuvenation are quantitatively describable in terms of the growth regime of the spin-glass coherence length.
By means of Monte Carlo simulations on the three-dimensional Ising spin-glass model, we have studied aging phenomena with various temperature(TTT)-change protocols. Particularly, a TTT-shift protocol, in which a system is first quenched to and aged for a period tw1t_{\rm w1}tw1​ at a temperature T1T_1T1​, and subsequently aged at a new temperature T2T_2T2​ is closely investigated. Most importantly, the mean size of domains, which is extracted from the replica-overlap function, was found to grow monotonically without any appreciable decrease by the TTT-change. We also found the relaxation of energy density and spin auto-correlation function during the TTT-shift process can be explained within the following picture: the dynamics finally crossovers to an isothermal aging of T2T_2T2​ at around t2≃tw1(eff)t_2 \simeq t_{\rm w1}^{\rm (eff)}t2​≃tw1(eff)​ after the TTT-change, where tw1(eff)t_{\rm w1}^{\rm (eff)}tw1(eff)​ is an effective waiting time related with tw1t_{\rm w1}tw1​, but in the transient regime t2<tw1(eff)t_2 \lt t_{\rm w1}^{\rm (eff)}t2​<tw1(eff)​, adjustment of the population of thermally active droplets from that at T1T_1T1​ to T2T_2T2​ takes place very slowly. Implications of the results on aging phenomena in other TTT-change protocols such as TTT-cycling and continuous TTT-change with an intermittent stop observed by simulations as well as experiments are discussed.
We study numerically the nonequilibrium dynamics of the three-dimensional Heisenberg Edwards-Anderson spin glass submitted to protocols during which temperature is shifted or cycled within the spin glass phase. We show that (partial) rejuvenation and (perfect) memory effects can be numerically observed and study both effects in detail. We quantitatively characterize their dependences on parameters such as the amplitude of the temperature changes, the time scale at which the changes are performed, and the cooling rates used to vary the temperature. We contrast our results both to those found numerically in the Ising version of the model, and to experimental results in different samples. We discuss the theoretical interpretations of our findings, arguing, in particular, that ``full'' rejuvenation can be observed in experiments even if temperature chaos is absent.
The slow nonequilibrium dynamics of the Edwards-Anderson spin-glass model on a hierarchical lattice is studied by means of a coarse-grained description based on renormalization concepts. We evaluate the isothermal aging properties and show how the occurrence of temperature chaos is connected to a gradual loss of memory when approaching the overlap length. This leads to rejuvenation effects in temperature shift protocols and to rejuvenation-memory effects in temperature cycling procedures with a pattern of behavior parallel to experimental observations.
The aging phenomena in Ising spin glasses in a magnetic field are investigated both by the numerical simulation on three-dimensional Ising Edwards-Anderson model and by the experiment on the Fe0.55Mn0.45TiO3 Ising spin glass. After reviewing our recent numerical work on the field-shift aging protocol, by which we argue that the spin-glass (SG) phase is unstable in a static magnetic field of any strength, we present the nonequilibrium aspects of the field-cooled magnetization in a relatively small field observed numerically and experimentally. The results are compatible with the absence of the equilibrium SG phase in a field.