  Interactions among neighboring birds in a flock cause an alignment of their
flight directions. We show that the minimally structured (maximum entropy)
model consistent with these local correlations correctly predicts the
propagation of order throughout entire flocks of starlings, with no free
parameters. These models are mathematically equivalent to the Heisenberg model
of magnetism, and define an "energy" for each configuration of flight
directions in the flock. Comparing flocks of different densities, the range of
interactions that contribute to the energy involves a fixed number of
(topological) neighbors, rather than a fixed (metric) spatial range. Comparing
flocks of different sizes, the model correctly accounts for the observed scale
invariance of long ranged correlations among the fluctuations in flight
direction.
