ErgodicNonErgodic Transition Phenomena in Condensed Matters
Project/Area Number  01540298 
Research Category 
GrantinAid for General Scientific Research (C)

Allocation Type  Singleyear Grants 
Research Field 
物性一般（含極低温･固体物性に対する理論）

Research Institution  University of Tsukuba 
Principal Investigator 
TAKAYAMA Hajime University of Tsukuba Institute of Physics Prof., 物理学系, 教授 (40091475)

CoInvestigator(Kenkyūbuntansha) 
NEMOTO Koji University of Tsukuba Institute of Physics Research Associate., 物理学系, 助手 (60202248)

Project Period (FY) 
1989 – 1990

Project Status 
Completed(Fiscal Year 1990)

Budget Amount *help 
¥2,200,000 (Direct Cost : ¥2,200,000)
Fiscal Year 1990 : ¥1,100,000 (Direct Cost : ¥1,100,000)
Fiscal Year 1989 : ¥1,100,000 (Direct Cost : ¥1,100,000)

Keywords  ErgodicnonErgodic transition phenomenon / meanfield theory for spin glasses / naive meanfield model / marginal stability of the spin glass phase / overlap function of metastable states / EA model / reentrant transition / Griffiths' phase in spin glass / ナイブ平均場模型 / スピングラス / 自由エネルギの多谷構造 / 状態間重なりの確立分布関数 / スピングラス・強磁性転移 
Research Abstract 
Some condensed matters, such as spin glasses, exhibit an ErgodicnonErgodic 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 meanfield theory for spin glasses. In the present research project, we have extensively analyzed the naive meanfield (NMF) model by solving its equations of states numerically, and have obtained the following results. 1) We introduce a class of meanfield 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 phasespace 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 reentrant transition are also clarified. The EA model with shortranged 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.

Report
(3results)
Research Output
(8results)