Temperature dependence of the spin susceptibility of a clean Fermi gas with repulsion

Spin susceptibility of a clean Fermi gas with repulsion in any dimension is considered using a supersymmetric low energy theory of interacting spin excitations and renormalization scheme recently proposed by Aleiner and Efetov. We generalize this method to include the coupling to the magnetic field. As a result, we obtain for the correction delta chi to the Pauli susceptibility a nonanalytic temperature dependence of the form Td-1 gamma(2)(b)(T) in dimensions d=2, 3, where gamma(b)(T) is an effective d-dependent logarithmically renormalized backscattering amplitude. In one dimension, delta chi is proportional to gamma(b)(T), and we reproduce a well known result obtained long ago by a direct calculation.