Glassy Dynamics in Random Spin Systems

自旋玻璃中的老化现象作为最典型的玻璃化动力学，已经得到了广泛的研究。用蒙特卡罗方法对它们在Edwards-Anderson(EA)模型中的各个方面进行了数值模拟。大多数模拟结果都被液滴图像很好地解释了：老化现象与极慢的平衡有关，这是由热激活过程引起的，并以自旋玻璃(SG)相干长度(或SG磁区的平均尺寸)R(Tw)在系统快速淬火到低温SG相后的时间tw的增长规律表示。此外，我们还用R(Tw)和L(T)确定了各个量的标度表达式，后者是在t的时间尺度内激发的液滴的平均尺寸。更明确地说，我们发现了以下结果：1)通过对零场冷磁化强度的模拟，发现即使在温度为c…的情况下，R(Tw)也会累积增长更多的人在SG阶段被挂起。将从模拟中提取的增长规律直接应用于时间尺度比模拟大10个数量级以上的实验ZFCM测量时，ZFCM数据依赖于R(Tw)的泛函。这是关于老化现象的实验和模拟之间的第一次直接和定量的一致。2)深入研究了四维EA模型的等温时效过程，首次发现大部分结果，包括R(Tw)的生长规律，都可以用液滴理论很好地描述。此外，在R(Tw)和L(T)相当的时间范围内，液滴的激发能变得反常地小。我们认为，这一事实是实验观测到的零场冷磁化强度与零场冷磁化强度不同的原因。3)通过交流磁化率考察了3D EA模型中的温移老化过程，并根据R(Tw)和L(T)的模拟结果验证了各种标度表达式。在模拟中还首次发现了混沌(返老还童)效应的前兆。较少

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