Title

Study of universal behavior for the single-impurity Kondo problem

Date of Award

1991

Availability

Article

Degree Name

Doctor of Philosophy (Ph.D.)

Department

Physics Physiology and Biophysics

First Committee Member

Stewart E. Barnes, Committee Chair

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.

Keywords

Physics, Electricity and Magnetism; Physics, Condensed Matter

Link to Full Text

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