  A phenomenon can hardly be found that accompanied physical paradigms and
theoretical concepts in a more reflecting way than magnetism. From the
beginnings of metaphysics and the first classical approaches to magnetic poles
and streamlines of the field, it has inspired modern physics on its way to the
classical field description of electrodynamics, and further to the quantum
mechanical description of internal degrees of freedom of elementary particles.
Meanwhile, magnetic manifestations have posed and still do pose complex and
often controversially debated questions. This regards so various and utterly
distinct topics as quantum spin systems and the grand unification theory. This
may be foremost caused by the fact that all of these effects are based on
correlated structures, which are induced by the interplay of dynamics and
elementary interactions. It is strongly correlated systems that certainly
represent one of the most fascinating and universal fields of research. In
particular, low dimensional systems are in the focus of interest, as they
reveal strongly pronounced correlations of counterintuitive nature. As regards
this framework, the quantum Hall effect must be seen as one of the most
intriguing and complex problems of modern solid state physics. Even after two
decades and the same number of Nobel prizes, it still keeps researchers of
nearly all fields of physics occupied. In spite of seminal progress, its
inherent correlated order still lacks understanding on a microscopic level.
Despite this, it is obvious that the phenomenon is thoroughly fundamental of
nature. To resolve some puzzles of this nature is a key topic of this thesis.
(excerpt from abstract)
