Nonanalytic behavior of the spin susceptibility in clean Fermi systems

The wavevector and temperature dependent static spin susceptibility, \chi_s(Q,T), of clean interacting Fermi systems is considered in dimensions 1\leq d \leq 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\ln|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 1-d systems, as well as for the temperature dependence of \chi_s(Q=0) in d=3.