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

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 $h\to 0$. 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.

20 pages, 3 figures, accepted for publication in New Journal of Physics