Abstract
We compute the effective dispersion and vibrational density of states (DOS) of two-dimensional subregions of three-dimensional face-centered-cubic crystals using both a direct projection-inversion technique and a Monte Carlo simulation based on a common underlying Hamiltonian. We study both a (111) and (100) plane. We show that for any given direction of wave vector, both (111) and (100) show an anomalous regime at low where is the energy associated with the given mode and is its wave number. The scaling should be expected to give rise to an anomalous DOS, , at low : rather than the conventional Debye result: . The DOS for (100) looks to be consistent with , while (111) shows something closer to the conventional Debye result at the smallest frequencies. In addition to the direct projection-inversion calculation, we perform Monte Carlo simulations to study the effects of finite sampling statistics. We show that finite sampling artifacts act as an effective disorder and bias , giving a behavior closer to than . These results should have an important impact on the interpretation of recent studies of colloidal solids where the two-point displacement correlations can be obtained directly in real-space via microscopy.
7 More- Received 18 September 2014
DOI:https://doi.org/10.1103/PhysRevE.90.062309
©2014 American Physical Society