Singularity of the density of states for one-dimensional chains with random couplings

Abstract

We prove that the density of states for the tight-binding model with off-diagonal disorder under general conditions diverges forR→0 at least as\( \sim \frac{1}{{\left| E \right|(\ln \left| E \right|)^4 }}\). This result is established through the study of the recurrence properties of an associated Markov chain.