Two Types Of Disordered The Hmf Model Of The Dynamics Studies

In the multiparticle system.the macroscopic behavior of particles not only can be got by the statistical average of the statistical mechanics,can also be simulated by classical dynamics.With the rapid development of computer technology and mature, dynamical method which is used for the studying of phase transition with the multiparticle sys-tems,has been become a viable and effective study method that is used more widely in recent years.In this thesis,we mainly study the equilibrium phase transition problems with long-range interaction systems by classical dynamics. our main work is as follows:First,we introduce the global coupled Hamiltonian Mean Field(HMF) model where all the particles interact with others with the same coupling strength J=1.By dynamics,we get the transition temperature and critical energy Tc=0.5, uc= 0.75.It's consistent well with the theoretical analysis'.This is also proving the feasibility of the dynamical method which is used for the studying of phase transition.Considering the HMF model is a simplified ideal model,but in the real physical world,the interaction of the each particles in the system are often much more complex.In this regard.the HMF model is generalized to disordered HMF model.In the system,considering the coupling strength between the particles which rotate on a unit circle are different,we put the coupling coefficients are Jij,which is the coupling strength between i and j.we discuss the phase transitional with the random distribution of the Jij.There are two cases as follows:the first case is that we get the coupling coefficient Jij between 0 and 1. Compared with the HMF model,we find that the critical temperature and energy are decreased.We also discuss the case of 1< Jij< 2,and find the system's critical energy Uc>0.75.It imply that the system's critical energy is correlate with the Jij.When Jij decreased,the system is easily to have the phase transition.When Jij≡1.the model returns to the HMF model.The other case is that there are negative coupling interactions in the system,and its distribution p(Jij)=cδ(Jij+J0)+(1-c)δ(Jij-J0). We discuss the different distributions which how to influence the system's phase transition.With the study, it imply that the system's phase transition is relevant to c.When c is lager,the system has the lower critical temperature.when c.= 0.5,the system has no phase transition. Meanwhile,in a sense analogous to the Heisenberg-Mattics model,we get the Mattics-like HMF model.In this model, the points' disorder are used to instead the rods, ascribes Joξiξj replace Jij.where,ξi=±1, the probability is c(1-c). By dynamics,as P(ξi)= (1-c)δ(ξi+1)+cδ(ξi-1),the phase transition temperature and critical energy with the system have been studied on the different probability value c. It's found that the system's phase transition is relevant to c, the c is larger,the critical temperature and energy are higher. When c=1,the model returns to the HMF,and as c decreases,it's critical temperature and energy are gradually reduced.When c=0.5,it will not the phase transition.we also study the coupling strength J0 which how to influence the system's phase transition.It imply that when J0 is larger, the stronger of the particles couple with others in the system,it's critical temperature and energy are higher.