Excess Vibrational Modes and the Boson Peak in Model Glasses
  The excess low-frequency normal modes for two widely-used models of glasses were studied at zero temperature. The onset frequencies for the anomalous modes for both systems agree well with predictions of a variational argument, which is based on analyzing the vibrational energy originating from the excess contacts per particle over the minimum number needed for mechanical stability. Even though both glasses studied have a high coordination number, most of the additional contacts can be considered to be weak. 
Ning Xu, Matthieu Wyart, Andrea J. Liu, and Sidney R. Nagel