Universality class in the one-dimensional localization problem

Weak disorder behavior of the Lyapunov exponent is investigated for a one-dimensional disordered system whose band structure and transfer matrix form are manifestly different from the standard ones encountered in tight-binding models. For diagonal disorder, the critical exponents governing the divergence of the localization length at zero disorder are identical with those predicted for tight-binding models. For off-diagonal disorder, a new exponent is found in one of the band edges, indicating a different universality class. The scaling functions near the different band edges are displayed, and their values for zero arguments are not identical at all edges.