The Panic Model: Flocking with Minimal Cooperativity

TL;DR

This paper introduces a minimal 2D lattice model of self-propelled spins that only change direction upon collision, demonstrating robust flocking behavior and stripe formation even with minimal cooperativity.

Contribution

It presents a simple lattice model showing flocking with minimal interaction, and analyzes the dynamical transition using an order parameter.

Findings

Flocking occurs at nearly all densities despite minimal cooperativity.

Long stripe formations emerge in the system.

Dynamical analysis of the order parameter reveals transition details.

Abstract

We present a 2D lattice model of self-propelled spins that can only change direction upon collision with another spin. We show that even with ballistic motion and minimal cooperativity, these spins display robust flocking behavior at nearly all densities, forming long bands of stripes. The structural transition in this system can be characterized by an order parameter, and we demonstrate that if this parameter is studied as a dynamical variable rather than a steady-state observable, we can extract a detailed picture of how the flocking mechanism varies with density.