Delocalized vibrations in classical random chains

Normal modes of one-dimensional disordered chains with two couplings, one of them assigned at random to pairs in an otherwide perfect chain, are investigated. We diagonalize the dynamical matrix to find the normal modes and to study their spatial extent. Multifractal analysis is used to discern clearly the localized or delocalized character of vibrations. In constrast to the general viewpoint that all normal modes in one-dimensional random chains are localized, we find a set of extended modes close to a critical frequency, whose number increases with the system size and becomes independent of the defect concentration.