Monte Carlo Simulation Of Magnetic Structure At Finite Temperature

Nowadays magnetic materials play a very important role in the development of science and technology.In order to explore the characteristics of magnetic materials at finite temperature,many theories and methods have been proposed.Monte Carlo method as a numerical method,has been widely and effectively applied in this field.In this paper,the Metropolis algorithm of Monte Carlo method was used to simulate three-dimensional Ising model,three-dimensional Heisenberg model and a real magnetic material CrO₂.The main contents of this thesis are as follows:In the first chapter,different kinds of spin interactions in magnetic systems and the historical development are introduced.In the second chapter,we introduce some basic knowledge of phase transition and two frequently used boundary conditions.In the third chapter,the history and basic principle of Monte Carlo method are introduced.We give the details of the Monte Carlo method,especially the Metropolis algorithm.In the fourth chapter,we introduced the background of Ising model,and explaine how to use the Metropolis algorithm to simulate the three-dimensional Ising and Heisenberg models.Comparing the calculated results,the difference in Heisenberg model simulation is emphasized.Finally,the Curie temperature of the two models are given,respectively.In the fifth chapter,we briefly introduce the structure and properties of magnetic material CrO₂,and explain two methods of constructing body-centered cubic structure.Then,comparing the results obtained by the two methods with those obtained by the software vampire to validate our results.At last,we obtained accurate Curie temperature by calculating local average susceptibility.In the last chapter,the main work of this thesis is briefly summarized,and we we give some comments on further in-depth study.