Universality Class Of Non-equilibrium Phase Transitions Based On Forget-remember Mechanism

In recent decades,non-equilibrium critical phenomena has aroused a lot of research interests.Similar to equilibrium critical phenomena,universality is still a main tool for exploring a variety of non-equilibrium phase transition systems.All systems belonging to the same universality class own the same set of critical exponents and scaling functions.Similar to equilibrium critical phenomena,many non-equilibrium phase transitions can be categorized into different universal classes.So we need to study each of them individually.It is very compelling to study the universal behaviours of these systems,which may lead to the deep understandings of their interconnections and controls of such systems.Resembling to equilibrium phase transitions,the mean field method is accurate only above the critical dimensions Dc for non-equilibrium transitions.Compared with the series expansion and the renormalization group methods,the application of numerical simulation method is more widely adopted for phenomenological studies of universality class.This thesis was based on the Monte Carlo(MC)simulations for the study of the universality class of forget-remember mechanism(FRM)model of epidemic spreading on lattice,aiming to prove that the FRM model of epidemic spreading belongs to the directed percolation(DP)universality class.In this work,we started from introducing the elementary concepts in phase transitions and critical phenomena,with subsequent brief introductions to scaling theory,universality and renormalization group theory.Then we introduce a particular class of non-equilibrium phase transitions,with typical manifestation of being active to absorbing transitions.This work focuses on the directed percolation universality class of being active to absorbing phase transitions.The main task of this thesis is to calculate the steady state density p of the(1 + 1)-dimensional directed percolation,which changes over time.By analyzing the asymptotic dependence of p against time t,we can obtain the percolation threshold pc,and the exponent ?;in addition,we can use the data collapse method to obtain the values of v|| and v?.Through scaling relations,we can calculate the critical exponents ?,?|| and V?,as well as the other three critical exponents.To study the universal properties of the model of interest,we then applied the same method to get the critical exponents(?,v|| and v?)of(1+1)-dimensional forget-remember mechanism(FRM)model.By comparing the simulation results(critical exponents ?,v|| and v?)of these two models,we found that the corresponding critical exponents of(1+1)-dimensional FRM and DP model do agree with each other.Our analysis showed that the MC simulation results for FRM systems deviated slightly from those results for DP systems.This deviation of course can be explained by the fact that both systems contain different microscopic mechanisms and the finite size effects also play some roles.However,by adjusting the size of the selected system,the time steps and the size of the statistical ensemble,we can further reduce the deviation generated by the numerical simulations.It can be expected that a more accurate calculation result can be obtained by improving the performance of the calculation or utilizing more appropriate experimental conditions.In this thesis,the results showed that the two systems studied possess the same class of critical exponents,which indicates that the FRM spreading model belongs to the directed percolation universality class.This study can thus provide a good example for the verification of Grassberg's DP conjecture.