Monte Carlo simulation on aging processes within one `pure state' of the SK spin-glass model

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Abstract
Monte Carlo simulations on the SK model have been done to investigate aging processes after a rapid quench from to the spin-glass phase. Taking care of time ranges of simulation, we examine time evolutions of energy of the system, Parisi's overlap distribution function, auto-correlation and clones-correlation functions, distribution functions of the two correlations, and magnetization induced by the field applied after a certain waiting time. The data simulated exhibit a rich variety of aging phenomena. Most of them can be interpreted in a unified way, though qualitatively, by the scenario of growth of quasi-equilibrium domains which we have recently introduced. The results are consistent qualitatively with asymptotic behaviours of some of the basic assumptions and their results in recent analytical theory on the same SK model, so long as the limiting procedures in finite systems are taken properly. Also they suggest that a basin of attraction of one dominant pure state spans almost an entire phase space of the system with a common time-reversal symmetry.