Three-body Interactions Drive the Transition to Polar Order in a Simple Flocking Model

TL;DR

This paper demonstrates that three-body interactions are essential for the emergence of polar order in flocking models, especially at high densities, resolving discrepancies between theory and experiments.

Contribution

Introduces a solvable 1D flocking model showing three-body interactions are crucial for polar order, unlike binary interactions which are insufficient.

Findings

Binary interactions alone cannot produce polar order at high densities.

Three-body interactions enable the emergence of polar order in the model.

Non-Gaussian noise is necessary for binary interactions to generate order.

Abstract

A large class of mesoscopic or macroscopic flocking theories are coarse-grained from microscopic models that feature binary interactions as the chief aligning mechanism. However while such theories seemingly predict the existence of polar order with just binary interactions, actomyosin motility assay experiments show that binary interactions are insufficient to obtain polar order, especially at high densities. To resolve this paradox, here we introduce a solvable one-dimensional flocking model and derive its stochastic hydrodynamics. We show that two-body interactions are insufficient to generate polar order unless the noise is non-Gaussian. We show that noisy three-body interactions in the microscopic theory allow us to capture all essential dynamical features of the flocking transition, in systems that achieve orientational order above a critical density.