Aging Phenomena in Spin Glasses

通过扩大蒙特卡罗模拟的含义是关于3和4维度的EA模型，我们已经研究了在旋转玻璃上老化现象。phenomena are associated with the relaxation of a spin-glass （SG） system to equilibrium after it is rapidly quenched to a temperature below its transition temperature T_D2c_D2 The following results have been obtained。An isothermal aging process is the relaxation of the system after it is quenched to a temperature below T_根据对各种数量的模拟结果，如自旋自动相关功能和交互能量，它将此老化过程包括为平均激活过程中局部均衡状态域的增长过程，其中包括：而且物理量模拟的时间演变也很好地描述了由缩放表达式生成的水滴图片在SG上的描述。第一阶段：一个实验性温度转换协议是用来改变温度的 ... More to T型D22 after waiting for a period of t型D2 w1型D2 in the isothermal aging at T型D21型D2 ， and to observe subsequent aging of the system at T型D22型D2。根据我们的结果，我们提出了一个“域中的问题域”场景，以描述本协议中的老龄化过程。Namely， in each domain which has grown up by the first aging at T-D21-D2 and whose mean size is R（T-D2w1-D2）， droplet excitations，local equilibrated to T-D21-D2 just before the T-shift， relaxe to local equilibrium at T-D22-D2 （growth of 'quasi-domains'）。在“quasi-domains”的平均大小被抓到R（ty D2 w1 y D2），i. e，this re-equilibration has completed， the system becomes in a genuine isothermal process at t.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.本场景是基于一个模拟结果，即当该领域不断增长时，温度在SG阶段内发生了变化。The Scenario Consistenly Explains the memory effect Observed Experimentally。However，另一个有趣的现象，观察到的实验并称之为rejuvenation，但没有被当前模拟复制。这个问题是为未来的调查而提出的。Less（低）

By means of extensive Monte Carlo simulations on the 3 and 4 dimensional Ising EA models, we have studied aging phenomena in spin glasses. The phenomena are associated with the relaxation of a spin-glass (SG) system to equilibrium after it is rapidly quenched to a temperature below its transition temperature TィイD2cィエD2 The following results have been obtained.An isothermal aging process is the relaxation of the system after it is quenched to a temperature below TィイD2cィエD2. From the simulational results on various quantities, such as the spin auto-correlation function and the interaction energy, it is concluded that this aging process is regarded as the growth process of domains of locally equilibrated states by means of the thermally activated processes, and that time evolutions of the physical quantities simulated are well described by the scaling expressions which are derived form the droplet picture on the SG phase.An experimental temperature-shift protocol is to change temperature … More to TィイD22ィエD2 after waiting for a period of tィイD2w1ィエD2 in the isothermal aging at TィイD21ィエD2 , and to observe subsequent aging of the system at TィイD22ィエD2 . From our results simulated we have proposed the 'quasi-domains within domain' scenario to describe the aging process in this protocol. Namely, in each domain which has grown up by the first aging at TィイD21ィエD2 and whose mean size is R(tィイD2w1ィエD2), droplet excitations, locally equilibrated to TィイD21ィエD2 just before the T-shift, relaxe to local equilibrium at TィイD22ィエD2 (growth of 'quasi-domains'). After the mean size of the 'quasi-domains' catches up R(tィイD2w1ィエD2), i.e., this re-equilibration has completed, the system becomes in a genuine isothermal process at TィイD22ィエD2. This scenario is based on the simulational result that the domains grow continuously even when the temperature is changed within the SG phase. The scenario consistenly explains the memory effect observed experimentally. However, another interesting phenomenon, observed experimentally and called the rejuvenation, has not been reproduced by the present simulation. This problem is left for a future investigation. Less