Scaling properties of one-dimensional off-diagonal disorder

Abstract

Validity of the single parameter scaling (SPS) in one dimensional Anderson model with purely off-diagonal disorder is being studied. It is shown that the localized region with standard symmetry is divided into two regimes: SPS and non-SPS. Scaling relations of the Lyapunov Exponent are proposed for these two regimes. In the non-SPS regime, in additional to the localization length, there exists a new length scale which is related to the integrated density of states. A physical interpretation of the new length is the cross-over length which separates regions with chiral symmetry from those that have standard symmetry.