Novel type of phase transition in a system of self-driven particles

TL;DR

Numerical evidence is presented that this model results in a kinetic phase transition from no transport to finite net transport through spontaneous symmetry breaking of the rotational symmetry.

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 ($η$) added. We present numerical evidence that this model results in a kinetic phase transition from no transport (zero average velocity, $| {\bf v}_a | =0$) to finite net transport through spontaneous symmetry breaking of the rotational symmetry. The transition is continuous since $| {\bf v}_a |$ is found to scale as $(η_c-η)^β$ with $β\simeq 0.45$.