The wave vector and temperature-dependent static spin susceptibility, Xs(Q, T), of clean interacting Fermi systems is considered in dimensions 1 ≤ d ≤ 3. We show that at zero temperature Xs 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 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 for one-dimensional systems, as well as for the temperature dependence of Xs(Q = 0) in d = 3.
D. Belitz et al., "Nonanalytic Behavior of the Spin Susceptibility in Clean Fermi Systems," Physical Review B (Condensed Matter), vol. 55, no. 15, pp. 9452-9462, American Physical Society (APS), Apr 1997.
The definitive version is available at https://doi.org/10.1103/PhysRevB.55.9452
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