  Bond-disordered Anderson model in two dimensions on a square lattice is
studied numerically near the band center by calculating density of states
(DoS), multifractal properties of eigenstates and the localization length. DoS
divergence at the band center is studied and compared with Gade's result [Nucl.
Phys. B 398, 499 (1993)] and the powerlaw. Although Gade's form describes
accurately DoS of finite size systems near the band-center, it fails to
describe the calculated part of DoS of the infinite system, and a new
expression is proposed. Study of the level spacing distributions reveals that
the state closest to the band center and the next one have different level
spacing distribution than the pairs of states away from the band center.
Multifractal properties of finite systems furthermore show that scaling of
eigenstates changes discontinuously near the band center. This unusual behavior
suggests the existence of a new divergent length scale, whose existence is
explained as the finite size manifestation of the band center critical point of
the infinite system, and the critical exponent of the correlation length is
calculated by a finite size scaling. Furthermore, study of scaling of Lyapunov
exponents of transfer matrices of long stripes indicates that for a long stripe
of any width there is an energy region around band center within which the
Lyapunov exponents cannot be described by one-parameter scaling. This region,
however, vanishes in the limit of the infinite square lattice when
one-parameter scaling is restored, and the scaling exponent calculated, in
agreement with the result of the finite size scaling analysis.
