Exact Solution And Numerical Calculation Of The Mixed-spin Ising Model On A Decorated Bethe Lattice

Statistical models, which are the simplification of real system, cover the es-sential characteristics of system and play a very important role in the investigation of phase transition theory. All the equilibrium properties of the system can be de-termined by the thermodynamic functions and their macroscopic properties in the critical points which can be obtained by the calculation of the partition function of the simplified model. And Ising model is one of the simplest uniaxial discrete spin models. Though it is simple, it is very difficult to obtain the exact solutions and only some numerical results can be obtained for high-dimensional space.In this thesis, the ferrimagnetic mixed-spin Ising model on a decorated Bethe lattice with the coordination number q is exactly solved, and some critical proper-ties of the system are obtained. Specially, we have obtained some general conclu-sions about the critical temperature and magnetization for the system composed of q kinds of decorated spin. The main content of this thesis is as follows:In chapter1, we briefly introduce phase transitions and their classification, and review the mean field approximation of Ising model and the approach to solve one-dimensional Ising model.In chapter2, the critical temperature and magnetization of the system are obtained by solving the single spin Ising model on a Bethe lattice.In chapter3, we present an approach to solve the ferrimagnetic mixed-spin Ising model on a decorated Bethe lattice. This chapter is divided into three sec-tions according to the kind of the decorated spin. We find that the solutions of the third section will be equal to the first (second) section when there are one (two) kind(s) of decorated spin. The critical temperature and magnetizations of three different systems have been obtained. Some interesting results, for example, reen-trant phase transition and the non-monotonicity of the critical temperature, are presented in the figures in the first two sections. There are only some brief descrip-tions and discussions about the critical temperature and magnetization presented in the third section because of too many parameters.At last, we give the summary and outlook of this thesis.