Melting and Critical Phenomena in Two Dimensional Systems

(1)为了理解二维Wigner晶体在液体^4He表面的量子熔化，考虑了声子非调和性的影响。横向模色散关系的最低阶非谐波修正并不导致声子不稳定，与先前的计算相反，高阶修正是重要的。(2)研究了电子双纹波过程对液体^4H表面的影响，结果表明影响很小。(3)研究了一维两波段紧密结合模型在均匀电场中带间耦合强度变化时的电子态。结果表明，在高电场条件下，存在一组由不同波段产生的斯塔克阶梯。(4)考虑了二维强电场和强磁场下紧密结合模型的能谱。当电场与晶体对称轴成夹角作用时，特征能量子化，量子化的间隔等于最近相邻网线之间的势降，称为斯塔克阶梯谱。虽然能级距离随电场方向的改变而不连续变化，但态密度与电场方向无关。在带边缘附近打开意想不到的间隙，以获得适当的场强。当电场和磁场同时作用时，在适当的电场下，态密度呈阶梯状结构。讨论了物理起源。(5)分析了涡旋激励下二维系统的拓扑相变。引入涡量模量作为这类拓扑跃迁的一种新的序参量，并通过蒙特卡罗模拟研究了其性质。研究了二维XY（平面旋转体）模型、三角晶格海森堡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，在二维附近研究了三角形晶格反铁磁体的临界性质。通过蒙特卡罗模拟直接研究了XY和海森堡反铁磁体在三维堆叠三角形晶格上的临界性质。估计的指数和振幅比与实验结果吻合较好。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