  We study a disordered vibrational model system, where the spring constants k
are chosen from a distribution P(k) ~ 1/k above a cut-off value k_min > 0. We
can motivate this distribution by the presence of free volume in glassy
materials. We show that the model system reproduces several important features
of the boson peak in real glasses: (i) a low-frequency excess contribution to
the Debye density of states, (ii) the hump of the specific heat c_V(T)
including the power-law relation between height and position of the hump, and
(iii) the transition to localized modes well above the boson peak frequency.
