Moving and staying together without a leader

TL;DR

This paper introduces a minimal stochastic model for collective motion of particles that maintains cohesion through local interactions, revealing phase transitions and diffusive behaviors in flocking dynamics.

Contribution

It presents a new minimal model demonstrating how local noisy interactions can sustain cohesive flocking and explores the phase diagram and transition types.

Findings

Cohesion persists even at zero density in large flocks.

Identifies first-order phase transitions between different flocking states.

Analyzes diffusive properties related to flock shape and motion.

Abstract

A microscopic, stochastic, minimal model for collective and cohesive motion of identical self-propelled particles is introduced. Even though the particles interact strictly locally in a very noisy manner, we show that cohesion can be maintained, even in the zero-density limit of an arbitrarily large flock in an infinite space. The phase diagram spanned by the two main parameters of our model, which encode the tendencies for particles to align and to stay together, contains non-moving "gas", "liquid"' and "solid" phases separated from their moving counterparts by the onset of collective motion. The "gas/liquid" and "liquid/solid" are shown to be first-order phase transitions in all cases. In the cohesive phases, we study also the diffusive properties of individuals and their relation to the macroscopic motion and to the shape of the flock.