Heterogeneity promotes first to second order phase transition on flocking systems

Abstract

We have considered a variation of the Vicsek model with vectorial noise where each one of the agents have their own noise amplitude normally distributed around a mean value, $\mu$, with standard deviation $\sigma$. First-order phase transition are observed for standard deviation $0\leq\sigma<\sigma_{tri}\approx0.11$, whereas for larger values, up to $\sigma=0.3$, a continuous phase transition occurs. For values of $\sigma$ in the interval $0.15\leq\sigma\leq0.30$ the continuous nature of the observed transition is characterized by means of finite-size scaling techniques, that also allow us to estimate the exponents driving the transition. A study of bands stability suggests that no band can form in this regime. Inspired by biological facts, the perception heterogeneity introduced in the model trough $\sigma$, allow us to tune the collective behaviour of the system.