Study of electronic states with off-diagonal disorder in two dimensions

The nature of electronic states in a two-dimensional tight-binding model with off-diagonal disorder is examined by iterative methods applied to very long strips of finite width $M$. We find that for $E=0\mathrm{}$ the localization length depends linearly on $M$ for all disorders $W$. This indicates a $R^{-\gamma \mathrm{}\left(W\right)\mathrm{}}$ behavior of the wave function, and provides a singular deviation from the belief based on scaling theory that all states are exponentially localized in two dimensions. However, for all $E\ne 0$, states are exponentially localized and scaling behavior is obeyed.