  Numerical studies of amorphous silicon in harmonic approximation show that
the highest 3.5% of vibrational normal modes are localized. As vibrational
frequency increases through the boundary separating localized from delocalized
modes, near omega_c=70meV, (the "mobility edge") there is a
localization-delocalization (LD) transition, similar to a second-order
thermodynamic phase transition. By a numerical study on a system with 4096
atoms, we are able to see exponential decay lengths of exact vibrational
eigenstates, and test whether or not these diverge at omega_c. Results are
consistent with a localization length xi which diverges above omega_c as
(omega-omega_c)^{-p} where the exponent is p = 1.3 +/- 0.5. Below the mobility
edge we find no evidence for a diverging correlation length. Such an asymmetry
would contradict scaling ideas, and we suppose it is a finite-size artifact. If
the scaling regime is narrower than our 1 meV resolution, then it cannot be
seen directly on our finite system.
