  Electronic properties of disordered binary alloys are studied via the
calculation of the average Density of States (DOS) in two and three dimensions.
We propose a new approximate scheme that allows for the inclusion of local
order effects in finite geometries and extrapolates the behavior of infinite
systems following `finite-size scaling' ideas. We particularly investigate the
limit of the Quantum Site Percolation regime described by a tight-binding
Hamiltonian. This limit was chosen to probe the role of short range order (SRO)
properties under extreme conditions. The method is numerically highly efficient
and asymptotically exact in important limits, predicting the correct DOS
structure as a function of the SRO parameters. Magnetic field effects can also
be included in our model to study the interplay of local order and the shifted
quantum interference driven by the field. The average DOS is highly sensitive
to changes in the SRO properties, and striking effects are observed when a
magnetic field is applied near the segregated regime. The new effects observed
are twofold: there is a reduction of the band width and the formation of a gap
in the middle of the band, both as a consequence of destructive interference of
electronic paths and the loss of coherence for particular values of the
magnetic field. The above phenomena are periodic in the magnetic flux. For
other limits that imply strong localization, the magnetic field produces minor
changes in the structure of the average DOS.
