Nonanalytic behavior of the spin susceptibility in clean Fermi systems

The wave vector and temperature-dependent static spin susceptibility, ${\mathrm{\chi }}_{\mathrm{s}}$(Q,T), of clean interacting Fermi systems is considered in dimensions 1⩽d⩽3. We show that at zero temperature ${\mathrm{\chi }}_{\mathrm{s}}$ is a nonanalytic function of |Q|, with the leading nonanalyticity being |Q${\mathrm{|}}^{\mathrm{d}\mathrm{-}1}$ for 1${\mathbf{Q}}^2$ln |Q| for d=3. For the homogeneous spin susceptibility we find a nonanalytic temperature dependence ${\mathrm{T}}^{\mathrm{d}\mathrm{-}1}$ for 1${\mathrm{\chi }}_{\mathrm{s}}$(Q=0) in d=3.