Using Monte Carlo simulations, we have studied isothermal aging of three-dimensional Ising spin-glass model focusing on quasi-equilibrium behavior of the spin auto-correlation function. Weak violation of the time translational invariance in the quasi-equilibrium regime is analyzed in terms of effective stiffness for droplet excitations in the presence of domain walls. Within the range of computational time window, we have confirmed that the effective stiffness follows the expected scaling behavior with respect to the characteristic length scales associated with droplet excitations and domain walls, whose growth law has been extracted from our simulated data. Implication of the results are discussed in relation to experimental works on ac susceptibilities.

Using Monte Carlo simulations, we have studied the relaxation of energy of the threedimensional Ising spin-glass model in aging process. Our finite-size-scaling analysis on the isothermal energy decay after the quench suggests strongly that the energy relaxes by coarsening of domain walls in agreement with the droplet theory. We have also evaluated relaxation times required for spin configurations in small systems, which are regarded as isolated droplets, to flip globally. The results support the fundamental assumption of the droplet theory that coarsening of domain walls, in case of spin glasses, is driven by successive nucleation of thermally activated droplets.KEYWORDS: spin glass, slow dynamics, aging, droplet theory §1. IntroductionIn recent years off-equilibrium dynamics, particularly aging dynamics, of spin glasses has attracted much attention theoretically, 1) numerically, 2) and experimentally.3, 4, 5) Many experiments have confirmed that the response to small dc/ac magnetic field after quenching the system below the spin-glass transition temperature T c shows aging effects persistently at least up to the largest possible time scale available in laboratories. On the side of theories, one of the most notable advances is the analytical theory 1, 6, 7) based on solvable mean-field spinglass models, which has provided non-trivial predictions on aging effects.Presumably one expects that the slow relaxation is caused by some underlying collective spin excitations in the system. In the case of ordering processes in nonrandom systems like the conventional Ising ferromagnet, the relaxational dynamics after quenching the system below the phase transition temperature is related to coarsening of domain walls which separate ordered domains of two different pure states.8) The typical size of the domains, R(t), at time t usually grows by a certain power law. This behavior can be directly studied, for instance by scattering experiments. The intriguing question is if such a picture of the coarsening of domain walls also holds for aging processes in spin glasses. Obviously, the above mentioned mean-field theory, which is exact only in infinitely large dimension, is not helpful in this respect. The domain picture based on the so-called droplet theory, 9,10,11,12) has provided an interesting phenomenology. However the pure states of spin glasses cannot be found in practice which makes it difficult to rationalize the domain picture in a direct way.In the present study, 13) we mainly focus on the energy * Present address: Hydrographic Department, Maritime Safety Agency, 5-3-1 Tsukiji, Chuo-ku, Tokyo 104-0045 * * E-mail: takayama@issp.u-tokyo.ac.jp relaxation in the 3-dimensional EA spin-glass model during the aging process simulated by Monte Carlo dynamics. The latter starts from arbitrary initial configurations at temperature T below T c which simulates instantaneous quench to T from T = ∞. We have found that the relaxation of energy can be explained consistently in terms of coarsening of domain walls as in the case of usua...

No abstract

No abstract