1992 Fiscal Year Final Research Report Summary
Melting and Critical Phenomena in Two Dimensional Systems
| Project/Area Number |
02640276
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
物性一般（含極低温･固体物性に対する理論）
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| Research Institution | Osaka University |
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Principal Investigator |
SAITOH Motohiko Osaka University, College of General Education, Professor, 教養部, 教授 (80012441)
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| Co-Investigator(Kenkyū-buntansha) |
KAWAMURA Hikaru Osaka University, College of General Education, Associate Professor, 教養部, 助教授 (30153018)
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| Project Period (FY) |
1990 – 1992
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| Keywords | Stark ladder / 2D electron system / Wigner crystal / quantum melting / topological transition / Triangular lattice magnet / Monte-Carlo method / critical phenomena |
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| 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
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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
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