Nonanalytic behavior of the spin susceptibility in clean Fermi systems

The wave vector and temperature-dependent static spin susceptibility, χₛ(Q,T), of clean interacting Fermi systems is considered in dimensions 1{}d{}3. We show that at zero temperature χₛ is a nonanalytic function of |Q|, with the leading nonanalyticity being |Q|^d-1 for 13, and Q²ln |Q| for d=3. For the homogeneous spin susceptibility we find a nonanalytic temperature dependence T^d-1 for 13. 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 χₛ(Q=0) in d=3.