Scaling properties of one-dimensional off-diagonal disorder

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