  We consider the response of the density of a fermion ensemble to an applied
weak static magnetic field. It is known that for non-interacting Fermi gas,
this response is fully characterized by the Fermi volume and the Berry
curvature on the Fermi surface. Here we show the same result holds for
interacting fermions, including Fermi liquid and non-Fermi liquid, to all
orders in perturbation theory. Our result relies only on the assumption of a
well-defined Fermi surface and the general analytic properties of quantum field
theory, and is completely model independent.
