Collective dynamics in a Vicsek model with Metropolis-based interactions

We investigate the collective dynamics of self-propelled particles using a variant of the Vicsek model in which the local alignment rule is replaced by a Metropolis-based interaction mechanism. In this formulation, interactions depend on the angular difference between particle velocities, interpreted as an energy-like quantity that determines the acceptance probability via a Metropolis criterion. Unlike the classical Vicsek model, which restricts interactions to a radius of interaction, our approach allows particles to interact independently of distance, based solely on directional alignment. We observe that the Metropolis rule gives rise to long-range correlations that persist even at high densities. In order to investigate the phase transition, we compute the order parameter, the Binder cumulant, and the susceptibility for both models. We find that the Metropolis rule shows stronger finite-size effects and sharper susceptibility peaks, suggesting a more abrupt transition, while the Vicsek model exhibits smoother behavior consistent with a continuous transition.