Nonanalytic behavior of the spin susceptibility in clean Fermi systems

The wave vector and temperature-dependent static spin susceptibitity, chi(s)(Q,T), of clean interacting Fermi systems is considered in dimensions 1 less than or equal to d less than or equal to 3. We show that at zero temperature chi(s) is a nonanalytic function of \Q\, with the leading nonanalyticity being \Q\(d-1) for 1<d<3, and Q(2)In\Q\ for d=3. For the homogeneous spin susceptibility we find a nonanalytic temperature dependence Td-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 fur one-dimensional systems, as well as for the temperature dependence of chi(s)(Q=0) in d=3.