  We study the energy cost of flocking in the active Ising model (AIM) and show
that besides the energy cost for self-propelled motion, an additional energy
dissipation is required to power the alignment of spins. We find that this
additional alignment dissipation reaches its maximum at the flocking transition
point in the form of a cusp with a discontinuous first derivative with respect
to the control parameter. To understand this singular behavior, we analytically
solve the two- and three-site AIM models and obtain the exact dependence of the
alignment dissipation on the flocking order parameter and control parameter,
which explains the cusped dissipation maximum at the flocking transition. Our
results reveal a trade-off between the energy cost of the system and its
performance measured by the flocking speed and sensitivity to external
perturbations. This tradeoff relationship provides a new perspective for
understanding the dynamics of natural flocks and designing optimal artificial
flocking systems.
