Nonanalytic behavior of the spin susceptibility in clean Fermi systems

The wave vector and temperature-dependent static spin susceptibility, χ_s(Q,T), of clean interacting Fermi systems is considered in dimensions 1<=d<=3. We show that at zero temperature χ_s is a nonanalytic function of \|Q\|, with the leading nonanalyticity being \|Q\|^d-1 for 1<d<3, and Q²ln \|Q\| for d=3. For the homogeneous spin susceptibility we find a nonanalytic temperature dependence T^d-1 for 1<d<3. We give qualitative mode-mode coupling arguments to that effect, and corroborate these arguments by a perturbative calculation to second order in the electron-electron interaction amplitude. The implications of this, in particular for itinerant ferromagnetism, are discussed. We also point out the relation between our findings and established perturbative results for one-dimensional systems, as well as for the temperature dependence of χ_s(Q=0) in d=3.