Aging Phenomena in Complex Systems

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Aging phenomena in random systems with frustration, or complex systems, have been extensively investigated more than a decade. They are infinitely long-time relaxation processes to equilibrium (but in some systems to a state different from equilibrium). Researches on the phenomena are expected to open a new field in statistical physics and condensed matter physics, namely, the out-of -equilibrium dynamics in such complex systems. In the course of this program aging phenomena and their related slow dynamics in spin-glasses were mainly studied. We obtained various interesting findings which provide us deeper insights into one of the most fundamental ingredients of the complex system, i.e., its rugged free-energy landscape in phase space.The main results obtained in this program are as follows.1) Parisi's overlap distribution function, which describes theoretically the hierarchical structure in the rugged free-energy landscape of spin-glasses, was extracted experimentally for the first ti … More me by measuring aging phenomena followed after change of magnetic field (Orbach). 2) The characteristic differences between aging phenomena in cluster spin-glasses and those in ordinary spin-glasses were found experimentally (Ito). 3) Based on the results by large-scale simulations a unified scenario (named Growth of Quasi-Equilibrium Domain one), for aging phenomena in the SK model of finite sizes was proposed (Takayama). 4) By the simulations on aging phenomena in the 3D Heisenberg spin-glass model the results, which imply the existence of the chiral-glass transition, were obtained for the first time (Kawamura). 5) The non-universal feature of the spin-glass transition that critical nature depends on the type of distribution of random interactions was found by numerical simulations (Campbell). 6) Various interesting perceptron models for on-line learning were proposed and investigated (Nishimori). 7) In heavy electron system Ce(Ru_<1-x>Rh_x)_2Si_2 three ground states, Fermi liquid, non-Fermi liquid, and antiferromagnetic ones, were specified and the quantum phase transitions between them were analyzed experimentally (Miyako, Ocio). Less