We consider a system of coupled classical harmonic oscillators with spatially fluctuating nearestneighbor force constants on a simple cubic lattice. The model is solved both by numerically diagonalizing the Hamiltonian and by applying the single-bond coherent potential approximation. The results for the density of states g(ω) are in excellent agreement with each other. As the degree of disorder is increased the system becomes unstable due to the presence of negative force constants. If the system is near the borderline of stability a low-frequency peak appears in the reduced density of states g(ω)/ω 2 as a precursor of the instability. We argue that this peak is the analogon of the "boson peak", observed in structural glasses. By means of the level distance statistics we show that the peak is not associated with localized states.
63.50.+xA ubiquitous and rather intriguing feature in the physics of glasses is the anomalous behavior of the low-frequency part of the vibration spectrum and the corresponding thermal properties [1][2][3]. While the origin of the linear lowtempature specific heat is commonly attributed to the existence of double-well potentials or two-level systems [4], there is still considerable debate about the so-called "boson peak". This peak shows up in the density of states (DOS) g(ω) as an excess contribution, compared to the usual Debye behaviour ( g(ω) ∝ ω 2 ). It is taken as being responsible for a number of features observed in specific heat and thermal conductivity measurements, as well as in Raman or neutron scattering data [1-3,5-8]. The boson peak seems also to persist at elevated temperatures. Here its relation to the liquid-glass transition and the corresponding relaxation dynamics is a matter of discussion [9][10][11][12][13]. Due to the development of new experimental techniques allowing to perform Brillouin scattering measurements in the THz range [14][15][16][17], as well as pertinent molecular dynamics simulations [18][19][20][21][22] the question concerning the nature of the modes in the boson peak region has gained much additional interest recently.Several models have been formulated to explain the physical origin of the boson peak. In the soft-potential model [23,24] the existence of anharmonic localized vibrations is postulated to be an intrinsic and essential property of amorphous systems. The scattering of propagating phonons by these modes is then taken as the origin for the excess DOS in the boson peak region.Another, almost orthogonal approach considers harmonic degrees of freedom solely. Here the scattering of phonons is associated with the disorder in the force constants, or, equivalently, spatially fluctuating elastic constants [25]. The first contribution in this direction has been the phonon-fracton approach [26,27], in which harmonic vibrational excitations on a percolating lattice were considered. However, a numerical simulation of this model [27] showed that the crossover from propagating modes (phonons) to localized fractal excitations (fractons) does not lead t...