Studies On The Magnetic Properties Of The Heisenberg Ferromagnetic Chain Within Callen Approximation

The investigation of magnetism materials has attracted increasing attention. In thelast one hundred years, researchers developed many experimental methods, theorical mod-els and theorical mechanism to discuss the magnetism of magnet. In these methods,Green's function method is considered as one of the better methods to investigate theproperties of magnet. It can be applied to all temperature areas, and it can get goodresults which agree with others'results. In this paper, we adopt Green's function toinvestigate the one-dimensional quantum ferromagnetic Heisenberg models.In the first chapter, the research background and contents of ferromagnetic modelshave been summarized brie?y, and a simply introduction of Green's function method hasbeen given.In the second chapter, the one-dimensional spin-1 ferromagnetic Heisenberg modelhas been investigated by Green's function method. We apply Green's function method tocope with the Hamiltonian of the system, and obtain the equations of motion of high-orderGreen's function chain. In order to obtain self-consistency equations, we use the Callenapproximation for the exchange interaction term. Through the spectral theorem, mag-netization and susceptibility are found to be as a function of the temperature, magneticfield. We also discuss the power laws of maximum susceptibilityχ(T_m) and temperatureT_m. Our results are in agreement with the other theoretical results.In the third chapter, theoretical calculations are carried out on the one-dimensionalspin-1/2 ferromagnetic Heisenberg model. We also apply Green's function method tocope with the Hamiltonian of the system, and use the modified Callen approximationfor the anisotropic term. We discuss the zero field susceptibility and correlation lengthverse temperature. According the results, we find our modified Callen approximation isbetter than random phase approximation and Callen approximation. Our results are inagreement with the other theoretical results.In the last chapter, a brief summary of this paper, including the theories and theresults, is given. The shortage and further research are also mentioned.