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 [cond-mat/0602309]. 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 non-analytic temperature dependence of the form $ T^{d-1}\gamma_{b}^{2}(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.