  The interest in the study of spin-Peierls phenomenon has increased with the
discovery of copper germanium oxide (CuGeO_3) as an example of spin-Peierls
systems. The availability of this inorganic compound as large, high quality
single crystals, allow experimental measurements which aid in understanding the
spin-Peierls phenomenon. This report details the numerical and analytical work
done on the various magnetic phases that occur in a quasi-one-dimensional
spin-Peierls system (like that of copper germanium oxide). Taking the system to
be finite, the bond displacements, single particle energies, energy
eigenfunctions, spin densities and phonon frequencies are calculated
numerically for all possible magnetizations, which includes both the
commensurate and incommensurate phases, at zero temperature. Solitons of
fractional spin are found to be present in the system for appropriate
magnetizations. The uniform to dimerized phase transition occurring in this
system is also modelled numerically. The single particle and ground-state
energies are later obtained theoretically for the uniform and dimerized phases.
In addition, the lattice spin displacements are analytically modelled for a
particular magnetization of the system.
