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 chi(parallel to) diverges, in the thermodynamic limit, like h(-nu) as h -> 0. In finite systems of linear size L, chi(parallel to) saturates to a value similar to 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.