Numerical Study on Aging Dynamics in the 3D Ising Spin-Glass Model. I. Energy Relaxation and Domain Coarsening

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Abstract
Using Monte Carlo simulations, we have studied the relaxation of energy of the three-dimensional 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, though the probability distribution function of the barrier free-energies, and so the growth law of domains, differ from what were assumed in the original droplet theory.
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