The Study Of Monte-Carlo Method On Extended XY Spin Model

Monte-Carlo method is a method of stochastic simulation with the development of computer technique. For the extensive stochastic phenomena in the nature, not only in traditional fields such as nuclear physics, statistical physics, molecule dynamics and so on that Monte-Carlo method has its extensive application, but also it is popularize and has great development in economics, demography and medicine.The Monte-Carlo method in statistical physics aims to study the model of equilibrium or nonequilibrium thermodynamics system by stochastic sampling computer simulation. Monte-Carlo method has two kinds of samplings: simple sampling Monte-Carlo method and importance sampling Monte-Carlo method. Metropolis method is a former importance sampling method. Since then, there are a series of improvements on this method. Many cluster algorithms such as Swenden-Wang method and Wolff method derive from this method. With a great profound understanding on Monte-Carlo method, a lot of new and effective methods will appear in the near future.As an important type of anisotropy, DM interaction has been attracted much attention in recent years. DM interaction plays an important role in the study of spin glasses as well as the emergence of weak ferromagnetism observed in the low temperature orthorbombic phase of lamellar copper oxide superconductors. The DM interaction has also been found to violate the crystal symmetry of quantum spin liquid system S r Cu 2 ( BO3 )2 in high magnetic field. Numerical simulation and experimentation study show that DM interaction can have on magnetic ordering in anti-ferromagnetic materials.KT phase transition which was caused by the unbinding of vortex-antivortex pairs, is found to be common in two dimensional XY model. The DM interaction can induce an easy-plane anisotropy, from which a KT transition is expected. In this paper, we study the thermodynamic and critical properties of two dimensional ferromagnetic XY model with DM interaction by using Metropolis method plus Swenden-Wang algorithm. We get the results as follows: (1) The effects of DM interaction on specific heat, susceptibility and magnetization are simulated. We get the plots of these physical quantities with the change of temperature; (2) Compared with the situation without DM interaction, we find that the chiral Z 2 symmetry of the DM interaction plays an important role in a two dimensional XY spin system. It is found that thermodynamic and magnetic properties and the phase transition are affected by the DM interaction since this special chirality;(3) We also study the correlation properties of our system and plot the integrated correlation time with temperature for different DM strength. We prove the fact that spin correlation is strong near the transition temperature. The superiority of cluster method is also proved.