Application Of Monte Carlo Method In Magnetic System

By using Monte Carlo simulation method, we studied Ferromagnetic Ising Model and Antiferromagnetic Heisenberg Model, these two models describe magnetic properties in classical and quantum separately.In chapter one, we introduced history of magnetic system, the development and application of magnetic materials, and structure of this paper.In chapter two, we introduced the history and basic notion of Monte Carlo simulation method, and also give the procedure of this method.In chapter three, three-dimensional Ferromagnetic Ising model was studied by using classical Monte Carlo method. We find that1, There is a ferromagnet-paramagnet phase transition in three-dimensional Ising model without exterior magnetic field, and Critical point of phase transition is J / kTc=0.2224(or Tc=4.4964J/k, J for exchange integral ,k for Boltzmann constant).2, When exterior magnetic field was applied, the phase transition phenomenon will disappear, there is only paramagnetic magnetization, and energy approach to same at high temperature. With exterior magnetic field increasing, Energy will decrease in low temperature, therefore the maximum value of specific heat and susceptibility will decrease and the corresponding temperature will decline.In chapter four, the Antiferromagnetic Heisenberg model with spin 1/2 on a square lattice was simulated by using the Stochastic Series Expansion Quantum Monte Carlo method. The results are as follows:1, Energy and magnetization will increase with increasing temperature for isotropy lattice without exterior magnetic field, specific heat have a maximum at kT/J=0.6 and uniform susceptibility saturates at kT/J=1. For anisotropy lattice without exterior magnetic field, energy and magnetization will decrease with anisotropic parameter g increasing, the maximum of specific heat declines then increases and correspondence temperature will increase, and the saturated value of uniform susceptibility goes down and its temperature increase.2, For isotropy and existence of exterior field case, energy declines, magnetization and uniform susceptibility increase with magnetic field increasing. And magnetization has a maximum between kT/J=0.5 and 1 and shows the shallow minimum at low temperatures. For anisotropy and existence of exterior field, energy decreases in low field and it increases in high field with parameter g increasing. Magnetization and uniform susceptibility increase with magnetic field increasing for g<1. For g>1 there is a critical magnetic field, magnetization and uniform susceptibility are zero under hc and increase with magnetic field increasing beyond critical magnetic field. And critical magnetic field increases with anisotropic parameter increasing.In chapter five, we give a survey of main conclusion of the paper and make prospect for the future work.