Study of Universal Behavior for the SingleImpurity Kondo Problem
Abstract
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 highmagnetic field, lowtemperature 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 fourthorder in coupling constant. Once again, this analysis is for the weakly interacting, highmagnetic field (still H<< D, the cutoff of the order of Fermi energy) and lowtemperature (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 (fourthorder in coupling constant), the magnetization equation is nonuniversal.
 Publication:

Ph.D. Thesis
 Pub Date:
 February 1991
 Bibcode:
 1991PhDT........62N
 Keywords:

 KONDO PROBLEM;
 Physics: Condensed Matter; Physics: Electricity and Magnetism