  Many attempts to explain the Boson peak in the vibrational spectra of glasses
consider models of a lattice of harmonic oscillators connected by spring
constants of varying strength and randomly distributed. However, in real
glasses one expects that some molecules will be connected to their neighbors by
more than one weak bond, so that a realistic model should consider oscillators
with several weak springs. In this paper, a t-matrix formalism is used to study
the effect of such correlated weak springs in a scalar model on a simple cubic
lattice with a binary distribution of spring constants. Our results, which are
confirmed by computer simulations, show that a concentration of c oscillators
with z weak springs and 6-z strong ones leads to a low frequency peak in the
reduced density of states (Boson peak) even when the total concentration of
weak springs cz is less than 10%., No such peak has been found at these low
concentrations in previously reported calculations which used effective medium
methods. For a given value of cz, this peak becomes more pronounced and moves
to much lower frequencies as z increases.
