Leading birds by their beaks: the response of flocks to external perturbations

TL;DR

This paper investigates how flocks of active particles respond to small external fields, revealing universal scaling laws for susceptibility that depend on system size and dimensionality, supported by theoretical analysis and simulations.

Contribution

It derives universal critical exponents for flock susceptibility to external fields, linking them to fundamental dynamical and roughness exponents, and confirms these predictions through simulations.

Findings

Susceptibility diverges as a power law with external field strength.

Finite system susceptibility scales with system size as a power law.

Predicted exponents are confirmed by simulations in 2D and 3D.

Abstract

We study the asymptotic response of polar ordered active fluids ("flocks") to small external aligning fields $h$. The longitudinal susceptibility $\chi_{_\parallel}$ diverges, in the thermodynamic limit, like $h^{-\nu}$ as $h \rightarrow 0$. In finite systems of linear size $L$, $\chi_{_\parallel}$ saturates to a value $\sim L^\gamma$. The universal exponents $\nu$ and $\gamma$ depend only on the spatial dimensionality $d$, and are related to the dynamical exponent $z$ and the "roughness exponent" $\alpha$ characterizing the unperturbed flock dynamics. Using a well supported conjecture for the values of these two exponents, we obtain $\nu = 2/3$, $\gamma = 4/5$ in $d = 2$ and $\nu = 1/4$, $\gamma = 2/5$ in $d = 3$. These values are confirmed by our simulations.