Nonanalytic magnetic response of Fermi and non-Fermi liquids

We study the nonanalytic behavior of the static spin susceptibility of two-dimensional fermions as a function of temperature and magnetic field. For a generic Fermi liquid, χs (T,H) =const+ c1 max {T, μB H}, where c1 is shown to be expressed via complicated combinations of the Landau parameters, rather than via the backscattering amplitude, contrary to the case of the specific heat. Near a ferromagnetic quantum critical point, the field dependence acquires a universal form χs -1 (H) =const- c2 H 3 2, with c2 >0. This behavior implies a first-order transition into a ferromagnetic state. We establish a criterion for such a transition to win over the transition into an incommensurate phase.