Dynamic spin susceptibility of interacting electron systems

We study the dynamic spin susceptibility of interacting electrons in spatial dimensions from one to three. In all cases, backscattering processes result in non-zero imaginary part of the spin susceptibility above the particle-hole continuum of non-interacting electrons. In one dimension, we employ the renormalization group to go beyond the second order and obtain a general expression for the spin susceptibility. In higher dimensions, we show that the imaginary part of the spin susceptibility arises from the same mechanism as non-analytic corrections to the Fermi-liquid theory. We relate the obtained results to the lifetime of collective spin modes.