Research Of Monte Carlo Method And The Applications In Statistical Physics

We study the properties of three of condenced matter systems by using numerical method in thispaper. The classical Monte Carlo method and the Stochastic series expansions(SSE) Quantum MonteCarlo method are introduced and applied to investigate thermodynamic properties in three models,Ising model, antiferromagnetic Heisenberg model and hardcore Bose-Hubbard model.The thesis ia arranged as follow:The history and the application of superfluid and superconductor are first introduced in chapter one,the structure of the paper is also introduced in this chapter.In chapter two, we introduce the Monte Carlo method in detail, history, principal, characteristic andapplications in statistical physics.We apply the classical Monte Carlo method to simulate thermodynamic properties intwo-dimensional Ising model in chapter three.In chapter four, we specifically introduce the Stochastic series expansions Quantum Monte Carlomethod and the using it to simulate two-dimensional antiferromagnetic Heisenberg model.The Stochastic series expansions Quantum Monte Carlo method is employed to investigatethermodynamic properties of hardcore Bose-Hubbard model in two dimension space; it is specificallydescribed in chapter five. The two-dimensional hardcore Bose-Hubbard model can be mapped into thetwo-dimensional antiferromagnetic quasi-Heisenberg model under transform of bosonic operators.There will be an additional term which is proportional to the total number of sites comparing with realHeisenberg Model and it is difficult for simulation. Using a nonlocal “operator-loop update,” it allowsone to simulate thousands of sites.A brief summary is given in chapter six, in which we conclude the results of three modelsinvestigated in this paper and make prospect for the further investigation.