Glassy Dynamics in Random Spin Systems

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Aging phenomena in spin glasses, the most typical glassy dynamics, have been extensively studied. Their various aspects in the Edwards-Anderson (EA) model have been numerically examined by the Monte Carlo method. Most of the results simulated turn out to be well interpreted by means of the droplet picture : the aging phenomena associate with the extremely slow equilibration which is due to thermally-activated processes and is represented in terms of the growth law of the spin-glass (SG) coherence length (or the mean size of SG domains), R (tw), at time tw after rapid quench of the system to the low-temperature SG phase. Furthermore we have confirmed the scaling expressions of various quantities in terms of R (tw) and L (t), where the latter is the mean size of droplets excited within time scale of t. More explicitly, we have found the following results.1) By the simulation on the zero-field-cooled magnetization (ZFCM), R (tw) is found to cumulatively grow even when the temperature is c … More hanged within the SG phase. When its growth law extracted from the simulation is directly applied to the corresponding experimental ZFCM measurement whose time scale is larger by more than 10 orders of magnitude than the simulation, the ZFCM data turn out to lie on a universal function of R (tw). This is the first direct and quantitative coincidence between experiment and simulation on aging phenomena. 2) The isothermal aging process in the 4-dimensional (4D) EA model has been intensively studied, and it has been found for the first time that the most of the results, including the growth law of R (tw), are well described by the droplet theory. Furthermore, the droplet excitation energy is found to become anomalously small in the time range where R (tw) and L (t) are comparable. We have argued that this fact is the origin of difference between the ZFCM and field-cooled magnetization observed experimentally. 3) The temperature-shift aging process in the 3D EA model has been examined through the ac susceptibility, and various scaling expressions have been confirmed in terms of R (tw) and L (t) simulated. The precursor of the chaos (rejuvenation) effect has been also found for the first time in simulation. Less