Nonuniversality in the Kondo effect

We have analytically evaluated, up to fourth order, all logarithmic terms in the perturbation expansion of the magnetization scrM for the Kondo model. All nonlogarithmic terms have been evaluated up to third order. When these results are compared with the claimed universal function scrM(H/${\mathit{T}}_{\mathit{H}}$) calculated with the Bethe ansatz, we find that the two cannot be made to agree whatever the form of ${\mathit{T}}_{\mathit{H}}$. We conclude that such universal functions do not exist.