Phase Transition In Two-dimensional XY Model With Complicate Interactions And AC Ratchet Effect

In this thesis, we first study the AC ratchet effect for the XY model with asymmetric potential. The directed motion of vortices and antivortices driven by AC currents in the two-dimensional Josephson junction arrays with two kinds of asymmetric pinning potential are studied numerically. It is found that the rectifying voltage shows non-monotonic behavior and is strongly dependent on the vortex density and the amplitude of the AC currents. Based on the simulated vortex structures and appearance of vortex-antivortex pairs, the observed characteristics of DC voltage and the amplitude of the AC currents are well explained.Second, we investigate the XY model with complicate interactions nearest-neighbor biquadratic exchange interactions. In the simulation, we choose four representative parameter sets, which correspond to the four ground-state phases. For each parameter set, we measure several physical quantities, such as specific heat, magnetization, and magnetic susceptibility. In addition, the Binder cumulant is measured to locate the transition point. We find that the magnetic phase transitions occurs for Ferro and CF2, but the nematic configuration is always disordered; nematic and magnetic configurations are always disordered for Spiral(1,1); a sole nematic transition occurs while the magnetic configuration is always disordered for UUDD. For each phase transition, the specific heat displays a cusp and magnetic susceptibility is divergent at some points. These are just the characteristics of a second-order phase transition. Thus we conclude that the present model exhibits a second-order phase transition.