Unifying Interpretations of Phase Transitions in the Vicsek Model: Correlation Length as a Diagnostic Tool

Vicsek Model is widely used in simulations of dry active matter. We re-examined two typical phase transitions in the original Vicsek model by using the velocity correlation length. One is the noise-driven disordered-to-ordered phase transition driven by noise, which was initially considered as a second-order transition (continuous transition), but was later demonstrated by Chate's detailed study to be a first-order transition. The other one is the disordered-to-ordered phase transition driven by average distance between particles, which is a second-order transition and satisfies the hyper-scaling relation of continuous transitions. We have discovered the change of correlation length during transition indicates a critical point in continuous transition while not in the discontinuous situation. We have also provided a method to classify phase transitions in active matter systems by using the correlation length and summarized previous work within the same framework. Finally, we end up with a potential application in experiments of bactirial swarms and robotic swarms. We hope our work paves the way for both theory and experiment development of active matter.