Nonanalytic Magnetic Response of Fermi- and non-Fermi Liquids

We revisit the issue of the non-analytic dependence of the static spin susceptibility of a 2D Fermi liquid on temperature and a magnetic field, $\chi_s (T, H) = \chi_0 + A T f_\chi (\mu_B |H|/T)$. We show that in a generic Fermi liquid the prefactor $A$ is expressed via complex combinations of the Landau parameters, and does not reduce to the backscattering amplitude, contrary to the case of the specific heat $C(T, H)$. We show that this distinction with the specific heat is mostly relevant near a ferromagnetic QCP -- the non-analytic terms in $\chi_s (T,H) $ are less singular near QCP than those in $C(T, H)$.