We observe a singularity in the electronic properties of the Anderson Model
of Localization with bounded diagonal disorder, which is clearly distinct from
the well-established mobility edge (localization-delocalization transition)
that occurs in dimensions d>2. We present results of numerical calculations
for Anderson's original (box) distribution of onsite disorder in dimensions d
= 1, 2 and 3. To establish this hitherto unreported behavior, and to understand
its evolution with disorder, we contrast the behavior of two different measures
of the localization length of the electronic wavefunctions - the averaged
inverse participation ratio and the Lyapunov exponent. Our data suggest that
Anderson's model exhibits richer behavior than has been established so far.Comment: Correction to v1: Fig.3 caption now displaye
