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arXiv:cond-mat/9909228 · International Journal of Modern Physics C

NUMERICAL STUDY ON AGING DYNAMICS IN THE 3D ISING SPIN-GLASS MODEL — QUASI-EQUILIBRIUM BEHAVIOR OF SPIN AUTO-CORRELATION FUNCTIONS

H. TAKAYAMA, Hajime Yoshino, T. KOMORI

Published Dec 1, 1999• 3 citations
arXivHTMLPDF

Abstract

Using Monte Carlo simulations, we have studied aging phenomena in three-dimensional Gaussian Ising spin-glass model focusing on quasi-equilibrium behavior of the spin auto-correlation functions. Weak violation of the time translational invariance in the quasi-equilibrium regime is analyzed in terms of effective stiffness for droplet excitations in the presence of domain walls. The simulation results not only in isothermal aging but also in T-shift aging process. T-shift aging processes exhibit the expected scaling behavior with respect to the characteristic length scales associated with droplet excitations and domain walls in spite of the fact that the growth law for these length scales still shows a pre-asymptotic behavior compared with the asymptotic form proposed by the droplet theory. Implications of our simulational results are also discussed in relation to experimental observations.

DOI
10.1142/s0129183199001212

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Using Monte Carlo simulations, we have studied aging phenomena in three-dimensional Gaussian Ising spin-glass model focusing on quasi-equilibrium behavior of the spin auto-correlation functions. Weak violation of the time translational invariance in the quasi-equilibrium regime is analyzed in terms of effective stiffness for droplet excitations in the presence of domain walls. The simulation results not only in isothermal aging but also in T-shift aging process. T-shift aging processes exhibit the expected scaling behavior with respect to the characteristic length scales associated with droplet excitations and domain walls in spite of the fact that the growth law for these length scales still shows a pre-asymptotic behavior compared with the asymptotic form proposed by the droplet theory. Implications of our simulational results are also discussed in relation to experimental observations.
Using Monte Carlo simulations, we have studied isothermal aging of three-dimensional Ising spin-glass model focusing on quasi-equilibrium behavior of the spin auto-correlation function. Weak violation of the time translational invariance in the quasi-equilibrium regime is analyzed in terms of {\it effective stiffness} for droplet excitations in the presence of domain walls. Within the range of computational time window, we have confirmed that the effective stiffness follows the expected scaling behavior with respect to the characteristic length scales associated with droplet excitations and domain walls, whose growth law has been extracted from our simulated data. Implication of the results are discussed in relation to experimental works on ac susceptibilities.
Aging phenomena of short-range Ising spin glass models have been investigated using Monte Carlo simulations. It is found that in the low-temperature spin-glass phase the mean domain size exhibits a crossover from a power-law growth associated with the critical fluctuation at the transition temperature to slower growth inherent in the low-temperature phase. The temperature dependence of the growth law of the domain size can be almost explained by this crossover. We also find that the spin-autocorrelation function in the quasi-equilibrium regime follows the expected scaling behavior from the droplet theory expressed in terms of the mean domain size and a characteristic length scale of droplet excitations. Spin glasses (SG) exhibit characteristic slow dynamics below the SG transition temperature. 1)-3) Recently such slow dynamics, in particular aging phenomena, has been much attractive both in experimental and theoretical studies. Several attempts have been made so far to explain the slow dynamics. There are mainly two distinct
Aging phenomena of short-range Ising spin glass models have been investigated using Monte Carlo simulations. It is found that in the low-temperature spin-glass phase the mean domain size exhibits a crossover from a power-law growth associated with the critical fluctuation at the transition temperature to slower growth inherent in the low-temperature phase. The temperature dependence of the growth law of the domain size can be almost explained by this crossover. We also find that the spin-autocorrelation function in the quasi-equilibrium regime follows the expected scaling behavior from the droplet theory expressed in terms of the mean domain size and a characteristic length scale of droplet excitations.
Using Monte Carlo simulations, we have studied the relaxation of energy of the three-dimensional Ising spin-glass model in aging process. Our finite-size-scaling analysis on the isothermal energy decay after the quench suggests strongly that the energy relaxes by coarsening of domain walls in agreement with the droplet theory. We have also evaluated relaxation times required for spin configurations in small systems, which are regarded as isolated droplets, to flip globally. The results support the fundamental assumption of the droplet theory that coarsening of domain walls, in case of spin glasses, is driven by successive nucleation of thermally activated droplets.
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.
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.