Novel Type of Phase Transition in a System of Self-Driven Particles

Abstract

A simple model with a novel type of dynamics is introduced in order to investigate the emergence of self-ordered motion in systems of particles with biologically motivated interaction. In our model particles are driven with a constant absolute velocity and at each time step assume the average direction of motion of the particles in their neighborhood with some random perturbation $\left(\eta \right)$ added. We present numerical evidence that this model results in a kinetic phase transition from no transport (zero average velocity, $|{\mathbf{v}}_a|=0\mathrm{}$) to finite net transport through spontaneous symmetry breaking of the rotational symmetry. The transition is continuous, since $|{\mathbf{v}}_a|$ is found to scale as $({\eta }_c-\eta {)}^{\beta }$ with $\beta \simeq 0.45$.