Study on phase transition critical phenomena in group movement based on eigen microstate theory

Abstract

Group motion exists widely in nature. Physicists use abstract models, such as the Vicsek model, to simplify group motion to obtain universal laws. However, the order parameters and phase transition types that describe the characteristics of the Vicsek model system are still controversial. For example, how to characterize the order parameters and types of phase transitions that characterize the system. This paper starts with the eigen microstate method and studies the Vicsek model. First, the continuous phase transition in the system is deeply studied through scaling analysis, and two critical exponents about the noise are obtained. Second, considering the density effect, similar to the noise study, three eigen microstates in the Vicsek model are revealed through scaling analysis, showing discontinuous and continuous phase transitions. Moreover, it is proved that in the actual infinite system, continuous phase transition and discontinuous phase transition still exist. Finally, the experimental data under different noises and densities are obtained through a large number of numerical simulations, and the phase diagram of the Vicsek model is depicted.