Ergodic-NonErgodic Transition Phenomena in Condensed Matters

一些凝聚态物质，如自旋玻璃，表现出遍历-非遍历转变现象，即它们在相空间中的自由能结构在高温下有一个独特的谷，而在低温下有许多谷，它们之间有实质性的障碍。自旋玻璃的平均场理论首次描述了这种跃迁现象。在本研究项目中，我们通过数值求解朴素平均场（NMF）模型的状态方程，对其进行了广泛的分析，得到了以下结果：1)我们引入了一类NMF和SK模型都属于的平均场模型，并证明了它们都具有边缘稳定的自旋玻璃相，并伴有许多亚稳态。2)详细分析了NMF模型的亚稳态在相空间的统计组织，并首次通过相空间分析证实了亚稳态的重叠函数服从最初在复制空间中由参数导出的普适概率规律。这一证实包括有限磁场的情况。3)阐明了重入跃迁下亚稳态组织的特征。采用蒙特卡罗模拟方法研究了具有短程相互作用的EA模型，利用模态展开法分析了自旋的空间相关性，证实了Griffiths相的存在性。

Some condensed matters, such as spin glasses, exhibit an Ergodic-nonErgodic transition phenomenon, i. e., their free energy structure in phase space has a unique valley at high temperatures, while it has many valleys at low temperatures with substantial barriers between them. This type of transition phenomena has been first described by the mean-field theory for spin glasses. In the present research project, we have extensively analyzed the naive mean-field (NMF) model by solving its equations of states numerically, and have obtained the following results.1) We introduce a class of mean-field models, in which both NMF and SK models belong, and show that all of they have the spin glass phase, which is marginal stable and is associated with many metastable states.2) Statistical organization of metastable states in phase space of the NMF model are analyzed in detail, and confirm, for the first time by the phase-space analysis, that the overlap function of the metastable states obey the universal probability law first derived by arguments in the replica space. This confirmation includes the case with finite magnetic fields.3) The characteristic features of the organization of the metastable states under the re-entrant transition are also clarified.The EA model with short-ranged interactions has been also investigated by the Monte Carlo simmuration, by which spatial correlation of spins is analyzed by means of the mode expansion method, and the existence of Griffiths' phase is confirmed.