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Melting and Critical Phenomena in Two Dimensional Systems

Research Project

Project/Area Number 02640276
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 InstitutionOsaka University

Principal Investigator

SAITOH Motohiko  Osaka University, College of General Education, Professor, 教養部, 教授 (80012441)

Co-Investigator(Kenkyū-buntansha) KAWAMURA Hikaru  Osaka University, College of General Education, Associate Professor, 教養部, 助教授 (30153018)
Project Period (FY) 1990 – 1992
Project Status Completed (Fiscal Year 1992)
Budget Amount *help
¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 1992: ¥300,000 (Direct Cost: ¥300,000)
Fiscal Year 1991: ¥300,000 (Direct Cost: ¥300,000)
Fiscal Year 1990: ¥1,000,000 (Direct Cost: ¥1,000,000)
KeywordsStark ladder / 2D electron system / Wigner crystal / quantum melting / topological transition / Triangular lattice magnet / Monte-Carlo method / critical phenomena / ファインマンの径路積分法 / 2次元量子融解 / 電子ーリプロン相互作用 / シュタルク・ラダ- / トポロジカル相転移 / 渦 / フラスト-レ-ション / 2次元系の臨界現象 / ウィグナ-格子 / シュタルクラダ- / 2バンド強結合模型 / 2次元XY模型 / モンテカルロシミュレ-ション
Research Abstract

(1) In order to understand quantum melting of 2-dimensional Wigner crystals on the liquid^4He surface, the effects of phonon anharmonicity are considered. The lowest-order anharmonic corrections to the dispersion relation of the transverse mode do not lead to the phonon instability in contrast to the earlier calculations and higher order corrections are shown to be important. (2) Effects of two-ripplon processes of electrons on the liquid^4H surface are investigated, and shown to be small. (3) The electronic states of a one-dimensional two-band tight-binding model in a uniform electric field, in which the strength of the interband counpling is varied, are studied. The results for high electric fields indicate the existence of a set of Stark ladders arizing from the different bands. (4) The energy spectrum of the two-dimensional tight-binding model in strong electric and magnetic fields is considered. When the electric field is applied with the angle with the symmetry axis of the crysta … More l, the eigenenergy is quantized with an interval equal to the potential drop between the nearest neighbor net lines, which is called the Stark ladder spectrum. Though the level separation varies discontinuously with the change of the direction, the density of states is shown to be independent of the direction of the electric field. Unexpected gaps open near the band edges for appropicate field strength. When both electric and magnetic fields are applied, the density of states shows steplike structure for the appropriate electric field. Physical origin is discussed. (5) Topological phase transitions of two-dimensional systems with vortex excitations are analyzed. As a new type of order parameter of such topological transitions, a vorticity modulus is introduced and its behavior is studied by means of a Monte Carlo simulation. The 2D XY (plane rotator) model, triangular-lattice Heisenberg antiferromagnet and ferromagnetic Heisenberg model are studied and the results are analyzed based on a finite-size scaling theory. (6) Critical properties of triangular-lattice antiferromagnets are studied near two dimensions on the basis of a field theoretic nonlinear sigma model and the renormalizationgroup epsilon=d-2 expansion. Critical properties of XY and Heisenberg antiferromagnets on a 3D stacked-triangular lattice are also studied directly by extensive Monte Carlo simulations. The estimated exponents and the amplitude ratio are in good agreement with the experimental results. Less

Report

(4 results)
  • 1992 Annual Research Report   Final Research Report Summary
  • 1991 Annual Research Report
  • 1990 Annual Research Report
  • Research Products

    (29 results)

All Other

All Publications (29 results)

  • [Publications] T.NAKANISHI: "Stark Ladders in a Tow Dimensional Tight-Binding Model" Proceedings of the 21st lnternational Conference on the Physics of Semiconductors.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] T.NAKANISHI: "Electronic States of a Two-Dimenseional Tight-Binding Model in Electric and Magnetic Fields" Physica B. (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] M.KIKUCHI: "Free-Vortex Formation of the Plane Rotator Model" J.Magn.Magn.Mater.104-107. 227-228 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] H.KAWAMURA: "Free-Vortex Formation and Topological Phase Transitions of Two-Dimensional Spin Systems" Phys.Rev.B. (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] M.SAITOH: "YAMADA Comference XXX Electronic Properties of Two-Dimensional Systems" YAMADA Science Foundation, 721 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] T. Kawaguchi: "Stark Ladders in a Two-Band Tight-Binding Model" J. Phys. Condens. Matter 3. 9371-9380 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] T. Kawaguchi: "Two-Ripplon Processes of Electrons on the Liquid^4He Surface" Surface Sci. 263. 671-673 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] T. Nakanishi: "Stark Ladders in a Two-Dimensional Tight-Binding Model" Proc. 21st Int. Conf. Phys. Sem. World Scientific.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] T. Nakanishi: "Electronic States of a Two-Dimensional Tight-Binding Model in Electric and Magnetic Fields" Physica. (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] H. Kawamura: "Chiral Ordering of XY Spin Glasses in Two and Three Dimensions---Domain-Wall Renormalization-Group Studies" J. Phys. Soc. Jpn. 60. 608-613 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] H. Kawamura: "Chiral Criticality near Two Dimensions" J. Phys. Soc. Jpn. 60. 1839-1843 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] H. Kawamura: "Monte Carlo Study of Chiral Criticality---XY and Heisenberg Stacked-Triangular Antiferromagnets" J. Phys. Soc. Jpn. 61. 1299-1325 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] H. Kawamura: "Chiral Ordering in Heisenderg Spin Glasses in Two and Three Dimensions" Phys. Rev. Lett. 68. 3785-3788 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] M. Kikuchi: "Free Vortex Formation of the Plane Rotator Model" J. Magn. Magn. Mater. 104-107. 227-228 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] H. Kawamura: "Free Vortex Formation and Topological Phase Transitions of Two-Dimensional Spin Systems" Phys. Rev. B47. 1134-1137 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] T.Nakanishi: "Stark Ladders in a Tow Dimensional Tight-Binding Model" Proceedings of the 21st International Conference on the Physics of Semiconductors(in press).

    • Related Report
      1992 Annual Research Report
  • [Publications] T.Nakanishi: "Electronic States of a Two-Dimensional Tight-Binding Model in Electric and Magnetic Fields" Physica B. (1993)

    • Related Report
      1992 Annual Research Report
  • [Publications] M.Kikuchi: "Free-Vortex Formation of the Plane Rotator Model" J.Magn.Magn.Mater.104-107. 227-228 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] H.Kawamura: "Free-Vortex Formation and Topological Phase Transitions of Two-Dimensional Spin Systems" Phys.Rev.B. (1993)

    • Related Report
      1992 Annual Research Report
  • [Publications] M.Saitoh: "Yamada Conference XXX Electronic Properties of Two-Dimensional Systems" Yamada Science Foundation, 721 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] T.Kawaguchi: "Stark Ladders in a TwoーBand TightーBinding Model" J.Phys.:Condens.Matter. 3. 9371-9380 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] T.Kawaguchi: "TwoーRipplon Processes of Electrons on The Liquid ^4He Surface" Surface Sci.263. 671-673 (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] M.Saitoh: "New Variational Bounds for the Free Energy in the Path Integral Method"

    • Related Report
      1991 Annual Research Report
  • [Publications] H.Kawamura: "Free Vortex Formation and Topological Phase Transition in Two Dimensions"

    • Related Report
      1991 Annual Research Report
  • [Publications] H.Kawamura: "Chiral Criticality near Two Dimensions" J.Phys.Soc.Jpn.60. 1839-1843 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] M.Saitoh: "Proceedings of the Ninth International Conference on the Electronic Properties of TwoーDimensional Systems" NorthーHolland, 721 (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] M.Saitoh: "Melting Criterion of TwoーDimensional Wigner Crystals on Thin Films of Liquid He." Surface Science. 229. 356-358 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] T.Kawaguchi: "Stark Ladders in a TwoーBand TightーBinding Model." Journal of Physics (Condensed Matter).

    • Related Report
      1990 Annual Research Report
  • [Publications] M.Kikuchi: "Free Vortex Formation in the TwoーDimensional XY Model."

    • Related Report
      1990 Annual Research Report

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Published: 1990-04-01   Modified: 2016-04-21  

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