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 δχ to the Pauli susceptibility a nonanalytic temperature dependence of the form T^d-1γ_b²(T) in dimensions d=2 , 3, where γ_b(T) is an effective d -dependent logarithmically renormalized backscattering amplitude. In one dimension, δχ is proportional to γ_b(T) , and we reproduce a well known result obtained long ago by a direct calculation.