Abstract
Ph.D. (Theoretical Physics)
In this thesis the thermodynamic and magnetic properties of
the non-degenerate Hubbard model are investigated. The underlying
lattice is the bcc-lattice. The results obtained will
therefore be especially applicable to systems with a single,
narrow conduction band.
As a check the thermodynamic properties of the model system
are first calculated in two limiting cases, namely the free
electron 'gas and the strong coupling limit. In this process,
use is made of results related to Wick's Theorem, which are
developed in an appendix. Another check is provided by the
calculation of the ground state spectrum of a finite, fourpoint
system. These results are obtained using standard group
theory techniques.
The ground state for the non-degenerate Hubbard model is solved
approximatively by a variational method. Once again the necessary
version of Wick's theorem is developed in an appendix. The ,results
for the neutral case (i.e. a half-filled band) is in agreement
with other studies on AB-lattices: It is found that the system
is anti ferromagnetic for all values of the coupling constant.
The quarter and three-quarter filled cases, hitherto not studied
because of numerical complexity, yield a completely different picture.
For increasing values of the coupling constant second order
phase transitions are found, first from the para- to the ferromagnetic
phase and then from the ferro- to the anti ferromagnetic phase.
The only results available in the literature related to this case
were obtained for an almost half-filled band in the strong-coupling
limit and qualitatively support the findings of the present study.
It is proposed that the simple theory used in this study be extended
for use in physical systems such as Cr.