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, chi(s)(T,H)=const+c(1) max{T,mu(B)parallel to H parallel to}, where c(1) 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 chi(-1)(s)(H)=const-c(2)parallel to H parallel to(3/2), with c(2)> 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.