Non-universality of critical exponents of a self-propelled particles system

• We have described the effect of the orientation zone on Vicsek model.
• We showed the non-universality of the Vicsek model.
• This study demonstrates the influence of orientation zone on the critical exponent's β and δ, indicating that these exponents are not universals.
• Our system exhibits a kinetic phase transition, from an ordered state, to a disordered state where the particles move in random directions.

The purpose of this paper is the study of the universality of the critical exponents β = 0.45 and δ = 0.35, detected in the Viscek model, under the effect of three zones (repulsion zone, orientation zone and attraction zone). Our aims are to understand more the behavior of non-equilibrium multi-agent system by extending the simple model proposed by Viscek et al. earlier for one zone. In our study, the particles corresponding to agents interact with their neighbors, by choosing at each time step a velocity va depending on their direction and perturbed by an external noise η. We demonstrate, by fixing the radius R1, R3 and by varying the radius R2 a phase transition can be obtained from disordered movement of individuals to highly align collective motion. The varied zone of orientation will be important for this research. Our findings confirm that the exponents β and δ depend on the size of orientation strongly indicate the non-universality of these critical exponents. This investigation is performed over different situations via a numerical simulation.