Logarithmic temperature contributions to long-wavelength spin susceptibility from particle-particle scattering

Abstract

Based on a second-order perturbation calculation with a δ-function interaction, Geldart and Rasolt have recently shown that the long-wavelength static spin susceptibility is nonanalytic in T at low temperatures. We find the nonanalyticity is suppressed by the summation of particle-particle scattering terms to all orders. Commonly held analyticity assumptions regarding the long-wavelength and low-temperature behavior of the susceptibility are thus not invalidated. We suggest that for the nonuniform susceptibility, a Kohn-Luttinger-Ward-like equivalence between the zero- and low-temperature perturbation series exists between classes of terms, rather than order by order.