Aging Phenomena in Complex Systems

具有挫折的随机系统或复杂系统中的老化现象已经被广泛研究了十多年。它们是达到平衡的无限长松弛过程（但在某些系统中达到与平衡不同的状态）。对这些现象的研究有望在统计物理学和凝聚态物理学中开辟一个新的领域，即这种复杂系统的非平衡动力学。在该程序中，主要研究了自旋玻璃中的老化现象及其相关的慢动力学。我们获得了各种有趣的发现，这些发现使我们对复杂系统的最基本成分之一有了更深入的了解，即相空间中崎岖的自由能景观。本程序取得的主要结果如下：1)首次通过实验提取了从理论上描述自旋玻璃粗糙自由能景观分层结构的Parisi重叠分布函数，并通过测量磁场变化后的老化现象（Orbach）。2)通过实验发现了团簇自旋玻璃与普通自旋玻璃中老化现象的特征差异（Ito）。3)基于大规模模拟结果，提出了有限尺寸SK模型中老化现象的统一情景（称为准平衡区域1的生长）（Takayama）。4)通过对三维Heisenberg自旋玻璃模型中老化现象的模拟，首次得到了手性-玻璃转变存在的结果（Kawamura）。5)通过数值模拟发现了自旋玻璃转变的非普遍特征，即临界性质取决于随机相互作用的分布类型（Campbell）。6)提出并研究了各种有趣的在线学习感知器模型（Nishimori）。7)在重电子系统Ce(Ru_<1-x>Rh_x)_2Si_2中，确定了费米液体、非费米液体和反铁磁三种基态，并对它们之间的量子相变进行了实验分析（Miyako, Ocio）。少

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