Absence of Anderson's transition in random lattices with off-diagonal disorder

Randomness is introduced in the off-diagonal elements of a tight-binding Hamiltonian. The question of localization is examined in this model Hamiltonian using two different methods: The localization function method and a self-consistent method based on an integral equation for the probability distribution of the self-energy. It is found, using both methods, that the presence of only off-diagonal randomness leaves the states in a finite region around the middle of the band always extended. Possible applications of this result are discussed.