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Using Monte Carlo simulations, we have studied aging phenomena inthree-dimensional Gaussian Ising spin-glass model focusing on quasi-equilibriumbehavior of the spin auto-correlation functions. Weak violation of the timetranslational invariance in the quasi-equilibrium regime is analyzed in termsof effective stiffness for droplet excitations in the presence of domain walls.The simulated results in not only isothermal but also $T$-shift aging processesexhibit the expected scaling behavior with respect to the characteristic lengthscales associated with droplet excitations and domain walls in spite of thefact that the growth law for these length scales still shows a pre-asymptoticbehavior compared with the asymptotic form proposed by the droplet theory.Implications of our simulational results are also discussed in relation toexperimental observations.Comment: 10 pages, 3 figure

NUMERICAL STUDY ON AGING DYNAMICS IN THE 3D ISING SPIN-GLASS MODEL — QUASI-EQUILIBRIUM BEHAVIOR OF SPIN AUTO-CORRELATION FUNCTIONS