Aging Phenomena in Spin Glasses

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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