Critical exponents of a self-propelled particles system

The Vicsek model of self-propelled particles is an important tool in the study of the collective motion of live organisms. The model consists of particles that move with a constant velocity and adopt, in a region called the zone of repulsion, the average motion direction of their neighbors disturbed by an external noise. A second-order phase transition from a disordered state, with motion in random directions, to an ordered motion state was observed. In this work, we have estimated, using finite-size scaling arguments, the critical exponents β, γ and ν of the original Vicsek model as a function of parameters important to the model, such as the orientation radius size, density, and velocity modulus. Our results show that the critical exponents depend greatly on these parameters.