Gregarious vs Individualistic Behavior in Vicsek Swarms and the Onset of First-Order Phase Transitions

TL;DR

This paper introduces an extension to the Vicsek Model by adding individualistic behavior, revealing that even a small amount of independence among particles can cause a first-order phase transition from order to disorder in flocking systems.

Contribution

The study demonstrates that incorporating individualistic motion into the Vicsek Model induces a first-order phase transition, highlighting new nonequilibrium phenomena in flocking behavior.

Findings

A small probability (~10%) of individualistic motion causes a phase transition.

The transition from ordered to disordered states is discontinuous (first-order).

The extended model preserves symmetry and interaction range but exhibits new critical behavior.

Abstract

The Standard Vicsek Model (SVM) is a minimal nonequilibrium model of self-propelled particles that appears to capture the essential ingredients of critical flocking phenomena. In the SVM, particles tend to align with each other and form ordered flocks of collective motion; however, perturbations controlled by a noise term lead to a noise-driven, continuous order-disorder phase transition. In this work, we extend the SVM by introducing a parameter $\alpha$ that allows particles to be individualistic instead of gregarious, i.e. to choose a direction of motion independently of their neighbors. By focusing on the small-noise regime, we show that a relatively small probability of individualistic motion (around 10%) is sufficient to drive the system from a Vicsek-like ordered phase to a disordered phase. Despite the fact that the $\alpha-$extended Model preserves the O(n) symmetry, the interaction range, as well as the dimensionality of the underlying SVM, this novel phase transition is found to be discontinuous (first-order), an intriguing manifestation of the richness of the nonequilibrium flocking/swarming phenomenon.