  Effects of the bond dilution on the critical temperatures, phase diagrams and
the magnetization behaviors of the isotropic and anisotropic quantum Heisenberg
model have been investigated in detail. For the isotropic case, bond
percolation threshold values have been determined for several numbers of two
(2D) and three (3D) dimensional lattices. In order to investigate the effect of
the anisotropy in the exchange interaction on the results obtained for the
isotropic model, a detailed investigation has been made on a honeycomb lattice.
Some interesting results, such as second order reentrant phenomena in the phase
diagrams have been found.
