Second Wilson number from third-order perturbation theory for the symmetric single-impurity Kondo model at low temperatures

We determine the impurity-induced free energy and the impurity-induced zero-field susceptibility of the symmetric single-impurity Kondo model from weak-coupling perturbation theory up to third order in the Kondo coupling at low temperatures and small magnetic fields. We reproduce the analytical structure of the zero-field magnetic susceptibility as obtained from Wilson’s renormalization group method. This permits us to obtain analytically the first two Wilson numbers.