Noise-induced Phase Transition in the Vicsek Model through Eigen Microstate Methodology

Abstract This paper presents a comprehensive framework for analyzing phase transitions in collective models such as the Vicsek model under various noise types. The Vicsek model, focusing on understanding the collective behaviors of social animals, is known due to its discontinuous phase transitions under vector noise. However, its behavior under scalar noise remains less conclusive. Renowned for its efficacy in the analysis of complex systems under both equilibrium and non-equilibrium states, the eigen microstate method is employed here for a quantitative examination of the phase transitions in the Vicsek model under both vector and scalar noises. The study finds that the Vicsek model exhibits discontinuous phase transitions regardless of noise type. Furthermore, the dichotomy method is utilized to identify the critical points for these phase transitions. A significant finding is the observed increase in the critical point for discontinuous phase transitions with escalation of population density.