Ergodic-NonErgodic Transition Phenomena in Condensed Matters

某些凝聚态物质，如自旋玻璃，表现出遍历-非遍历的转变现象，即：例如，它们在相空间中的自由能结构在高温下具有唯一的谷，而在低温下具有许多谷，谷之间具有实质性的势垒。这种类型的转变现象已经首先由自旋玻璃的平均场理论描述。本文通过数值求解朴素平均场（NMF）模型的状态方程，对NMF模型进行了深入的分析，得到了如下结果：1）引入了NMF模型和SK模型所属的一类平均场模型，并证明了它们都具有自旋玻璃相，2）详细分析了NMF模型相空间中亚稳态的统计组织，首次通过相空间分析证实，亚稳态的重叠函数服从由复型空间中的自变量首先导出的普适概率律。3）阐明了重入跃迁下亚稳态组织的特征，并对具有短程相互作用的EA模型进行了MonteCarlo模拟，用模展开法分析了自旋的空间相关性，证实了Griffiths相的存在。

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.