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

Monte-Carlo methods are probability methods for solving various kinds of computational problems by using random numbers, as opposed to deterministic algorithms. Over the past 50 years, with the appearing of computer and the development of the science and technology, this method has been raised as a independent algorithm. It is also applied in the experiment and the development of the nuclear weapon. In recent years, Monte-Carlo method is more regarded by people. It becomes one of the most important methods in computer simulations. Scientists have solved various problems using stochastic simulation.The phase transition of quantum spinning system with DM interaction is one of the most focal problems in condensed matter physics and counted physics. This interaction not only exists in antiferromagnetic materials but also exists in ferromagnetic materials. It has a very important influence on system properties. It also displays some new properties on this system sometimes.Frustrated XY model is more complex than classical XY model in spin interactions in the system. J₁ - J₂XY model is one kind of the frustrated XY model. In this thesis, we study the thermodynamic and critical properties of two dimensional ferromagnetic J₁-J₂XY model with DM interaction by using Metropolis method. We get the results as follows: (1) The effects of the next-nearest-neighbor pairs of the lattice with weak 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 J₂interaction, we find that the thermodynamic,magnetic properties and the phase transition are affected by the J₂ interaction; (3) We also study the correlation properties and plot the integrated correlation time with temperature for different J 2strength.