Correlated weak bonds as a source of the Boson peak in glasses

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.