Study Of The Phase Transition In Quenched Disorder System On Small World Networks

The effects of quenched disorder on the phase transition of system are very important in theory and practical application.Recently,the critical phenomenon of physical models defined on complex networks attracts lots of attention of many researchers.In this thesis,the effects of the topology of the small world networks on the quantum transition of the quenched disorder system are studied and the main results are as follows:The quantum phase transition of the dilute quantum Ising model in transverse field on the small world networks is studied.There are two quantum transitions:at low dilution,below the percolation threshold,there is a phase transition which is in the universality class of the generic random quantum Ising transition.Right at the percolation threshold,there is a finite range of transverse field strengths at which the system remains critical.This is another quantum transition in a different universality class.The properties of the second transition are determined largely by the statistics and geometry of the percolating clusters about which much information is available. The two transitions meet at a multicritical point.The critical behavior near the second quantum transition of the system is studied. Considering the contribution of the local large clusters,we calculate the dynamic susceptibility of the system.The results show that the smallest energy gap is an exponential function of the linear dimension of the rare large cluster at the critical point,which implies the presence of the activated dynamical scaling.And in the ordered and disordered phases in the vicinity of the transition,the system is gaplessness,which means the appearance of the strong power law Griffiths singularities at the no-critical point.The infinite critical point shifts with the change of the concentration of the shortcuts on the small world networks.And we give the exact values of the critical exponents using the relation between the exponents at the infinite disorder critical point of the system and at the percolation threshold of the small world networks.These exponents are constant,not dependent on the concentration of the random long-range connected bonds.This implies that the system shows a mean field behavior at the infinite disorder critical point.