Study of universal behavior for the single-impurity Kondo problem

Abstract

First, the magnetization equation {\cal M}\sb{i}={\cal M}\sb{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 $H\ll D,$ the cutoff of the order of Fermi energy) and low-temperature $(T\ll H)$ regime.Comparison between {\cal M}\sb{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.</p