  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.
