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 x_∥ diverges, in the thermodynamic limit, like h^-ν as h → 0 . In finite systems of linear size L, x_∥ saturates to a value ∼L_γ. 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.