Research On Dynamic Characteristics Of Mixed Spin Ising Model On Complex Networks

In recent years,complex networks have attracted much attention of scientists and become one of the hot topics in many scientific fields such as mathematics,mechanics,physics,computer science,life science,management science,systems science,sociology,finance and economics.The dynamics or evolution of physical state on complex networks becomes an important issue,and the investigation on the phase transition in spin systems on complex networks is a new direction with significant importance.The spin system on complex network is coined by assigning some kind of spin and interaction each site and edge of a complex network,respectively.This kind of spin systems can be employed to describe the dynamics of the spreading of diseases and rumors on complex networks,and other social problems.Therefore,the study of the phase transition of the spin systems on complex networks has important significance,which might be the base for its application in the above mentioned topics.Based upon the Metropolis important sampling of Monte Carlo method,this dissertation investigate the phase transition behaviors of the mixed spin Ising model on the small world networks,the small world Sierpinski gasket networks,and the Sierpinski gasket,respectively.The main results are listed as follows:1.The numerical simulations show that there exists continuous phase transition in the mixed spin Ising model on the NW small world networks with any nonzero rewiring probability.The critical temperature is affected by the crystal field and the rewiring probability,and a power low relation between the cirtical temperature and the rewiring probability is found.Mixed Spin Ising model and the conventional Ising model belongs to the same universality class,the critical exponent are ?=0,?=1/2,?=1,v=2.The critical temperature of the system is reduced to zero with the increasing of the crystal field.2.A kind of phase transition of the spreading of spin damage in Serpinski gasket is observed.The damage will hold when the temperature is below the transition temperature,and will heal when the temperature is above the transition temperature.The crystal field may change the transition temperature of the system.The increasing of the field strength results in the increasing of the probability of zero spins,and then enlarge the correlation length,which induces the decrease of the transition temperature.At a considerable high field strength,the damage disappears.Numerical simulation on the relaxation time of the damage spreading reveals that the static critical exponent Z is no longer a constant,but varies with the temperature and the crystal field.For a given crystal field,Z decreases with the increase of temperature.For a given temperature,it decreses with the increase of the field strength by a linear function.3.The small world Sierpinski gasket network is built by randomly re-adding edge in the traditional counterpart.It posses the properties of small world,self-similarity and scale-free.Based on Monte Carlo simulations,the magnetization,specific heat and fourth-order cumulant are calculated for the mixed spin system on this network.The result shows that the number of re-added edges directly influences the thermodynamic properties on this SWSG network,but does not lead to phase transition.The study on spread dynamic of spin shows that the relation between the relaxation time and system size is no longer a power law,but an exponential function.The static critical exponent Z is not a constant since the influence of the re-added edges.