Melting and Critical Phenomena in Two Dimensional Systems

(1)为了理解二维维格纳晶体在液氦表面的量子熔化，考虑了声子非谐性的影响。与以前的计算相反，对横模色散关系的低阶非谐修正并不会导致声子不稳定性，而高阶修正是重要的。(2)研究了电子在液体^4H表面的双涟漪过程，结果表明电子的双涟漪效应很小。(3)研究了均匀电场中一维两带紧束缚模型中带间计数强度变化时的电子态。高电场下的结果表明，存在一组来自不同能带的斯塔克阶梯。(4)研究了强电场和强磁场中二维紧束缚模型的能谱。当电场与…晶体的对称轴成一定角度时越L，本征能量被量子化的间隔等于最近邻网线之间的势降，这被称为斯塔克梯形谱。尽管能级间隔随方向的改变而不连续变化，但态密度与电场方向无关。在带边附近打开了意外的间隙，以获得合适的场强。当电场和磁场同时作用时，对于适当的电场，态密度呈现阶梯状结构。对物理起源进行了讨论。(5)分析了具有涡旋激励的二维系统的拓扑相变。作为这种拓扑转变的一种新型序参数，引入了涡度系数，并用蒙特卡罗模拟方法研究了它的行为。研究了二维XY(平面旋转体)模型、三角晶格海森伯反铁磁体模型和铁磁海森堡模型，并基于有限尺寸标度理论对结果进行了分析。(6)基于场论非线性Sigma模型和重整化群epsilon=d-2展开，研究了三角形晶格反铁磁体在二维附近的临界性质。用蒙特卡罗模拟直接研究了XY和Heisenberg反铁磁体在三维堆积三角形晶格上的临界性质。估算的指数和幅值比与实验结果吻合较好。较少

(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