Magnetic Phase Transitions and Critical Phenomena of Two-Dimensional Systems

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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.