Study Of Three Dimensional XY Model With Single-Spin Transition Dynamics

The introduction of the whole thesis is the first chapter. At the beginning we summarize some methods applied to the XY model in the previous research work and some properties of the system attained. The two-dimenstional XY model undergoes an unusual Klosterlitz-Thouless phase transiton at low temperature,where the system magnetization still vanishes but there is an quai-long order with the spin configuration like the vortex pair. With respect to the three-dimensional XY model which attracts the most attention of our latter work's,we introduced the spin wave theory and the self-consistent mean-field theory applied in it.In the second chapter,we introduce some theory about the transition dynamics which will be exercised in our latter research for the three-dimensional XY model. Glauber had initiated the investigation of the transition dynamics for spin system and developed the single-spin flipping critical dynamics. In recent years this theory has been improved to the single-spin transition dynamics which can be applied in the discrete spin system or the continuous spin system. The improved theory have succeeded in applying to Gaussian model.In the third chapter,based on the single-spin transition dynamics,we discuss the time evolution of the local magnetization in the anisotropic three-dimensional XY model under the zero external field. With the decoupling average technique and high-temperature approximation,we obtain the graph of the system magnetization evolving,which clearly exhibit the critical slowing phenomena of XY model near the phase transition region. And then,we specially study the effect of spin interaction's anisotropy on the critical temperature Tc. From what we have observed we suggest that the critical temperatur Tc grows as the anisotropy intensifies,while the system magnetization becomes weaker. The system becomes ID if the anisotropy ratio r goes to infinity,and its equilibrium state keeps zero magnetization at any finite temperature,which confirm that there is no observable transition for ID system.In the four chapter,as in the second chapter which based on the single-spin transition dynamics,we study the evolution of the system magnetization in thethree-dimensional XY model,which is subject to a time-dependent oscillating external field,and analyze its stationary states. We have found that there are two different stable states when the system is in the equillibrium. one is symmetric (or paramagnetic),where m oscillates around its Fourier component M = 0 along the time. Another is nonsymmetric (or ferromagnetic),where M 0. And in the (T,h) phase diagram there is a tricritical point,at which the two boundary lines of the paramagnetic and ferromagnetic regions merge. When w - 0 we obtain the static critical temperature Tc = 3.04.