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

TL;DR

This paper introduces a simple model of self-driven particles that exhibits a novel continuous phase transition from no movement to collective motion, driven by local interactions and symmetry breaking.

Contribution

The study presents a new model demonstrating a continuous phase transition in self-organized motion of particles with biologically inspired dynamics.

Findings

Identifies a kinetic phase transition from static to moving states.

Shows the transition is continuous with a specific scaling law.

Provides numerical evidence for spontaneous symmetry breaking.

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 ($\eta$) 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 $(\eta_c-\eta)^\beta$ with $\beta\simeq 0.45$.