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A dissertation submitted in fulfillment of the requirements for the degree of Master of Science in Physics at the University of the Witwatersrand. November 7th, 2016 / The spin-1=2 Kondo model describes an antiferromagnetic exchange interaction between an impurity spin and the spin-density of a Fermi gas. Although the thermodynamics of this system have been resolved, there are still some unanswered questions regarding its spatial features. The spatial region of correlation between the impurity spin and the spin-density of the Fermi gas is referred to as the Kondo screening cloud. For the case of anisotropic couplings, the cloud consists of four distinct components. In this dissertation we use the bosonization technique to derive both an exact numeric and an approximate analytic expression for the forward scattering longitudinal cloud at the Toulouse point. The expressions are then extended to incorporate the effects of a time-independent external magnetic field. The non-magnetic case displays universal scaling behavior, while the addition of an external magnetic field only slightly spoils the scaling in the vicinity of the crossover length (B) K , but remarkably not deep inside or outside the cloud. / MT2017

Mak Hon-lung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves [105]-107). / Abstracts in English and Chinese. / Abstract --- p.ii / Acknowledgements --- p.iii / Contents --- p.iv / List of Figures --- p.vii / List of Tables --- p.x / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- The origin of Heisenberg model --- p.1 / Chapter 1.2 --- High temperature superconductivity --- p.3 / Chapter 1.3 --- This project --- p.6 / Chapter Chapter 2. --- Studies of spin wave theory --- p.7 / Chapter 2.1 --- Introduction --- p.7 / Chapter 2.2 --- The uniform antiferromagnetic Heisenberg Model --- p.9 / Chapter 2.2.1 --- Linearization --- p.11 / Chapter 2.2.2 --- Quadratic equation --- p.15 / Chapter 2.2.3 --- Quadratic equation with Constraint --- p.20 / Chapter 2.2.4 --- Other results --- p.24 / Chapter 2.3 --- The anisotropic Heisenberg model --- p.29 / Chapter 2.3.1 --- The uniaxial model --- p.29 / Chapter 2.3.2 --- The XY Ferromagnetic model --- p.31 / Chapter Chapter 3. --- Theoretical approach --- p.35 / Chapter 3.1 --- Classical ground state --- p.35 / Chapter 3.2 --- Quantum fluctuation --- p.37 / Chapter 3.2.1 --- Linear combination of operators --- p.42 / Chapter 3.3 --- Calculation of physical quantities --- p.44 / Chapter 3.3.1 --- Zero mode problem --- p.48 / Chapter Chapter 4. --- Results of unfrustrated systems --- p.52 / Chapter 4.1 --- Introduction --- p.52 / Chapter 4.2 --- Uniform system --- p.52 / Chapter 4.3 --- Missing bond case --- p.55 / Chapter 4.4 --- Vacancy case --- p.58 / Chapter 4.5 --- Ferromagnetic impurity case --- p.61 / Chapter 4.6 --- Antiferromagnetic impurity case --- p.65 / Chapter 4.7 --- Abnormal antiferromagnetic bond case --- p.68 / Chapter Chapter 5. --- Ferromagnetic bond case --- p.71 / Chapter 5.1 --- Origin of ferromagnetic bond --- p.71 / Chapter 5.2 --- Numerical results --- p.72 / Chapter 5.2.1 --- The classical results --- p.72 / Chapter 5.2.2 --- Quantum corrections --- p.75 / Chapter 5.3 --- Results of other schemes --- p.76 / Chapter 5.3.1 --- Spin wave approach --- p.76 / Chapter 5.3.2 --- Other approaches --- p.77 / Chapter Chapter 6. --- The transmittance pattern in a necklace like system --- p.80 / Chapter 6.1 --- Introduction --- p.80 / Chapter 6.2 --- The model --- p.81 / Chapter 6.3 --- Ring configuration --- p.82 / Chapter 6.4 --- Chain configuration --- p.86 / Chapter 6.5 --- The transmittance pattern --- p.87 / Chapter 6.5.1 --- Constant and varying flux --- p.89 / Chapter 6.5.2 --- Random flux --- p.91 / Chapter 6.5.3 --- Constant impurity --- p.93 / Chapter 6.5.4 --- Some random effects --- p.96 / Chapter 6.6 --- Summary --- p.98 / Chapter 6.7 --- "Appendix, Derivation of basic equations " --- p.100 / Chapter Chapter 7. --- Conclusion --- p.103 / Bibliography --- p.105

Includes bibliographical references (p. 81).

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Thesis (Ph. D.)--University of Wisconsin--Madison, 1970. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

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The Néel temperatures of both the hydrated and 96% deuterated single crystal specimen of antiferromagnetic manganese chloride, have been compared. The sample was placed in the tank circuit of a radio-frequency oscillator; the inductance of the coil and hence the frequency of oscillation thus depended on the susceptibility of the specimen. As the crystal in the liquid helium bath was warmed through the Neel temperature, the oscillation frequency was monitored by a frequency counter. By this method, the Neel temperature could be deduced to change by -2.3% when the crystal was 96% deuterated. This result is comparable to the measurements on CoCl₂.6H₂O and CuCl₂.2H₂O. A semi-quantitative explanation proposes an intimate relationship between the superexchange interaction and the hydrogen bond strength. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

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