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Dynamics Associated with Metastable States in Random Systems

Research Project

Project/Area Number 60540227
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 物性一般(含極低温・固体物性に対する理論)
Research InstitutionKyoto University

Principal Investigator

TAKAYAMA Hajime  Research Institute for Fundamental Physics, Kyoto University, 基礎物理学研究所, 教授 (40091475)

Project Period (FY) 1985 – 1986
Project Status Completed (Fiscal Year 1986)
Budget Amount *help
¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 1986: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1985: ¥1,000,000 (Direct Cost: ¥1,000,000)
KeywordsMetastable states / TAP theory / Parisi's theory / Dynamical mean field theory of spin glasses / Gabay-Toulouse transition / Dynamics of CDW / Hysteretic phenomena
Research Abstract

1. Pure States and Parisi's Theory of the SK Spin Glass (SG) Model: A numerical method is established to find pure states, i.e., solutions for the TAP equations, of the SK model of a finite size. By the method the SG properties in the real spin space are examined in detail. On the other hand, a set of equations in Parisi's theory formulated in the replica spin space are also solved explicitly. Comparing both results obtained, we confirm quantitatively the basic relationships between the TAP theory and Parisi's one, and so make clear the unified picture of the SG transition within its mean field theory.
2. Magnetic Field Effects on the SG Transition: (1) At the Gabay-Toulouse transition of the m-vector SK model under static field h, the transverse nonlinear susceptibility is shown not to diverge so long as h=0. (2) By means of the dynamical mean field theory it is shown that the SG phase does exist in an ac external field, though the transition temperature is lowered by the field.
3. Dynamics of Charge-Density-Wave (CDW): Peculiar transport phenomena, observed in quasi 1D conductors and attributed to sliding motion of the CDW, are studied based on the Fukuyama-Lee-Rice (FLR) model, in which the CDW is regarded as classical deformable medium. (1) The results obtained by the perturbational expansion with respect to the pinning potential in the model are shown to agree with experimental results observed under large electric fields. (2) Extensive numerical simulations on 1, 2, and 3D FLR models are performed. They reproduce most of peculiar phenomena; dc nonlinear conduction, nonlinear dynamical phenomena such as the mode-locking, hysteretic phenomena revealing the existence of many metastable pinned states, and so on. The results confirm that these phenomena are characteristics of the FLR model, i.e., a nonlinear dynamical system with randomness.

Report

(1 results)
  • 1986 Final Research Report Summary
  • Research Products

    (22 results)

All Other

All Publications (22 results)

  • [Publications] Koji NEMOTO: J.Phys.C:Solid State Phys.18. L529-35 (1985)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Koji NEMOTO: J.Magn.Magn.Mater.54-57. 135-6 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Koji NEMOTO: Prog.Theor.Phys.75. 448-50 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Takayuki SHIRAKURA: J.Phys.C:Solid State Phys.19. L459-66 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Hiroshi MATSUKAWA: Physica. 143B. 30-2 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Hiroshi MATSUKAWA: Physica. 143B. 80-4 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Hiroshi MATSUKAWA: Synth.Metal. 19. 7-12 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Hajime TAKAYAMA: Prog.Theor.Phys.Suppl.87. 191-213 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Koji NEMOTO: J.Phys.C:Solid State Phys.(1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Hiroshi MATSUKAWA: J.Phys.Soc.Japan. (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Hiroshi MATSUKAWA: J.Phys.Soc.Japan. (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Koji NEMOTO: "TAP Free Energy Strucrure of SK Spin Glasses" J. Phys. C: Solid State Phys.18. L529-535 (1985)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Koji NEMOTO: "Structure of TAP Free Energy Surface of SK Spin Glasses (Numerical Study of Pure States)" J. Magn. Magn. Mater.54-57. 135-136 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Koji NEMOTO: "On the Transverse Nonlinear Susceptibility on the Vector SK Spin Glass in a Finite Field" Prog. Theor. Phys.75. 448-450 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Takayuki SHIRAKURA: "The Phase Transition of Spin Glasses in an External ac Field" J. Phys. C: Solid State Phys.19. L459-466 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Hiroshi MATSUKAWA: "Nonlinear AC and DC Conduction Phenomena of Charge-Density-Waves Described by Fukuyama-Lee-Rice Model" Physica. 143B. 30-32 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Hiroshi MATSUKAWA: "Numerical Study of Statics and Dynamics of Charge-Density-Waves Based on Fukuyama-Lee-Rice Model" Physica. 143B. 80-84 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Hiroshi MATSUKAWA: "Numerical Study on Statics and Dynamics of Charge-Density-Waves in Quasi 1D Conductors" Synth. Metal. 19. 7-12 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Hajime TAKAYAMA: "Dynamical Mean Field Theory of Spin Glasses and Their Phase Transitions in ac External Fields" Prog. Theor. Phys.Suppl. 87. 191-213 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Koji NEMOTO: "Numerical Study on Pure States of the SK Spin Glass Model Comparison with Parisi's RSB Solution" J. Phys. C: Solid State Phys.(1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Hiroshi MATSUKAWA: "Static and Dynamic Properties of Charge-Density-Waves Described by the Fukuyama-Lee-Rice Model. <I> . Perturbational Analysis and dc Nonlinear Properties" J. Phys. Soc. Japan. (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Hiroshi MATSUKAWA: "Static and Dynamic Properties of Charge-Density-Waves Described by the Fukuyama-Lee-Rice Model. <II> . Perturbational Analysis and dc+ac Combined Phenomena" J. Phys. Soc. Japan. (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary

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Published: 1987-03-31   Modified: 2016-04-21  

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