  Low temperature quantum corrections to the density of states (DOS) and the
conductivity are examined for a two-dimensional(2D) square crystal with
substitutional impurities. By summing the leading logarithmic corrections to
the DOS its energy dependence near half-filling is obtained. It is shown that
substitutional impurities do not suppress the van Hove singularity at the
middle of the band, however they change its energy dependence strongly. Weak
disorder due to substitutional impurities in the three-dimensional simple cubic
lattice results in a shallow dip in the center of the band. The calculation of
quantum corrections to the conductivity of a 2D lattice shows that the
well-known logarithmic localization correction exists for all band fillings.
Furthermore the magnitude of the correction increases as half-filling is
approached. The evaluation of the obtained analytical results shows evidence
for delocalized states in the center of the band of a 2D lattice with
substitutional impurities.
