A review is presented of the direct numerical approach to the study of the atomic vibrational properties of disordered systems. The basis and details of the numerical methods employed are first described. This is followed by a review of applications of the approach to two-component disordered lattices, glasses, mixed-crystal systems, orientationally disordered crystals, and random polymers.

DOI:https://doi.org/10.1103/RevModPhys.44.127