Numerical Study on Aging Dynamics in Ising Spin-Glass Models: Temperature-Change Protocols

By means of Monte Carlo simulations on the three-dimensional Ising spin-glass model, we have studied aging phenomena with various temperature($T$)-change protocols. Particularly, a $T$-shift protocol, in which a system is first quenched to and aged for a period $t_{\mathrm{w}1}$ at a temperature $T_1$, and subsequently aged at a new temperature $T_2$ 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 $T$-change. We also found the relaxation of energy density and spin auto-correlation function during the $T$-shift process can be explained within the following picture: the dynamics finally crossovers to an isothermal aging of $T_2$ at around $t_2\simeq t_{\mathrm{w}1}^{(\mathrm{e}\mathrm{f}\mathrm{f})}$ after the $T$-change, where $t_{\mathrm{w}1}^{(\mathrm{e}\mathrm{f}\mathrm{f})}$ is an effective waiting time related with $t_{\mathrm{w}1}$, but in the transient regime $t_2 \lt t_{\rm w1}^{\rm (eff)}$,adjustmentofthepopulationofthermallyactivedropletsfromthatat$T_1$to$T_2$ takes place very slowly. Implications of the results on aging phenomena in other $T$-change protocols such as $T$-cycling and continuous $T$-change with an intermittent stop observed by simulations as well as experiments are discussed.