Study of Universal Behavior for the Single-Impurity Kondo Problem

First, the magnetization equation { cal M}_{i}={cal M }_{i}(H) obtained by the application of Bethe Ansatz technique to the s - d exchange Hamiltonian, is expanded to fourth power in coupling constant, for the weakly interacting high-magnetic field, low-temperature regime. Next, a perturbative treatment of the s - d exchange model of the Kondo problem is presented. Calculations of the partition function and free energy are carried out, using conventional perturbation theory. This leads to a series expansion for the impurity magnetization, up to fourth-order in coupling constant. Once again, this analysis is for the weakly interacting, high-magnetic field (still H<< D, the cutoff of the order of Fermi energy) and low-temperature (T<< H) regime. Comparison between {cal M} _{i} obtained via Bethe Ansatz (where a cutoff scheme D is employed), to that obtained by application of conventional perturbation theory (where the momentum cutoff scheme ({cal D} scheme) is applied), enables one to examine universality of physical quantities. In particular, it will be established that once the calculations are carried to high enough order of perturbation theory (fourth-order in coupling constant), the magnetization equation is non-universal.