Phase Transition at Small-Medium Scales Vicsek Model Based on Eigen Microstate Method

Vicsek Model is widely recognized as one of the classic models for studying flocking problems. The presence of discontinuous phase transitions in the Vicsek Model under vector noise has been widely recognized, while there is no accepted consensus on whether the Vicsek Model under scalar noise has discontinuous phase transitions until now. The Eigen Microstate method has been applied to study complex systems such as natural climate, and it is suitable for studying both equilibrium systems and non equilibrium systems. The method of Eigen Microstate is used in this article to study the phase transition of the Vicsek model with scalar noise at small and medium-sized scales, and concludes that the standard Vicsek model has discontinuous phase transitions. And quantitative analysis was conducted to calculate the critical point of phase transition in the standard Vicsek model, and the relationship between the critical point and cluster density was summarized.