2 8 Ju n 20 01 Renormalized perturbation calculations for the single impurity Anderson model

We illustrate the renormalized perturbation expansion method by applying it to a single impurity Anderson model. Previously, we have shown that this approach gives the exact leading order results for the specific heat, spin and charge susceptibilities and leading order temperature dependence of the resistivity for this model in the Fermi-liquid regime, when carried out to second order in the renormalized interactioñ U. Here we consider the effects of higher order quasi-particle scattering and calculate the third order contributions to the H 3 term in the impurity magneti-zation for the symmetric model in a weak magnetic field H. The result is asymptotically exact in the weak coupling regime, and is very close to the exact Bethe ansatz result in the Kondo regime. We also calculate the quasi-particle density of states in a magnetic field, which is of interest in relation to recent experimental work on quantum dots.