Nonanalytic behavior of the spin susceptibility in clean Fermi systems
Abstract
The wavevector and temperature dependent static spin susceptibility, s(Q,T), of clean interacting Fermi systems is considered in dimensions 1≤ d ≤ 3. We show that at zero temperature s is a nonanalytic function of |Q|, with the leading nonanalyticity being |Q|d-1 for 1<d<3, and Q2|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 1-d systems, as well as for the temperature dependence of s(Q=0) in d=3.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.