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

We study the asymptotic response of polar ordered active fluids ("flocks") to small external aligning fields h. The longitudinal susceptibility χ∥ diverges, in the thermodynamic limit, like h−ν as h→0. In finite systems of linear size L, χ∥ saturates to a value ∼Lγ. The universal exponents ν and γ depend only on the spatial dimensionality d, and are related to the dynamical exponent z and the "roughness exponent" α characterizing the unperturbed flock dynamics. Using a well supported conjecture for the values of these two exponents, we obtain ν=2/3, γ=4/5 in d=2 and ν=1/4, γ=2/5 in d=3. These values are confirmed by our simulations.