Ergodic-NonErgodic Transition Phenomena in Condensed Matters

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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.