Magnetic Phase Transitions and Critical Phenomena of Two-Dimensional Systems

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，并结合适当的边界条件，采用蒙特卡罗模拟方法研究了涡量模量的性质。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。在XY模型的情况下，结果支持Kosterlitz-Thonless提出的理论，而在三角形反铁磁体的情况下，结果支持Kawamura和Miyashita提出的由Z_2 -涡驱动的有限温度拓扑转变的发生。基于场论非线性sigma模型和重整化群ε =d-2展开，研究了近二维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。研究了液氦表面二维电子系统中的电子-涟漪子相互作用。考虑二维超晶格，研究了强磁场和强电场作用下紧密结合模型的能谱。研究了强磁场作用下层状电子系统的输运特性。

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 sinulation combined with an appropriate type of boundary conditions. Two-Dimensional 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. In the case of the XY model, the results support a theory proposed by Kosterlitz-Thonless, while in case of triangular antiferromagnets, the results support the occurrence of a finitetemperature topological transition driven by Z_2 -vortices as suggested by Kawamura and Miyashita.Critical properties of triangular-lattice antiferromagnets are studied near two dimensions on the basis of a field theoretic nonlinear sigma model and the renormalization-group epsilon=d-2 expansion. Critical properties of XY and Heisenberg antiferromagnets on a three-dimensional 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.Electron-ripplon interactions in a two-dimensional electron system on liquid helium surface are studied.With a two-dimensional hyperlattice in mind, energy spectrum of tightbinding models under strong magnetic and electric fields are studied.Transport properties of layered electronic systems under strong magnetic fields are studied.