Excess modes in the vibrational spectrum of disordered systems and the boson peak - art. no. 064302

We study a disordered vibrational model system, where the spring constants k are chosen from a distribution P(k)proportional to l/k above a cut-off va lue k(min)>0. We can motivate this distribution by the presence of free vol ume in glassy materials. We show that the model system reproduces several i mportant features of the boson peak in real glasses: (i) a low-frequency ex cess contribution to the Debye density of states, (ii) the hump of the spec ific heat c(nu)(T) including the power-law relation between height and posi tion of the hump, and (iii) the transition to localized modes well above th e boson peak frequency.