Density of states for random-central-force elastic networks

Abstract

Effective-medium theory (EMT) results for the behavior of the elastic properties of random-central-force networks with a fraction p of nearest-neighbor bonds present are extended to finite frequencies. Good agreement with numerical simulations for the density of states at all frequencies is demonstrated. In particular, the gap at ${\omega }^2$=0 that opens up when p=$p^{\mathrm{*}}$, and the loss of elastic properties are correctly predicted. The fraction of zero-frequency modes is well described by the EMT and by constraint counting which leads to the same result. The only substantial error is that the EMT does not give Lifshitz tails at the band edges.