  We study a one-dimensional Frenkel Hamiltonian with off-diagonal disorder,
focusing our attention on the physical nature of the zero-energy peak of the
density of states. The character of excitonic states (localized or delocalized)
is also examined in the vicinity of this peak. It is shown that the state being
responsible for the peak is localized. A detailed comparison of the
nearest-neighbor approach with the long-range dipole-dipole coupling is
performed.
