Scaling of the non-phononic spectrum of two-dimensional glasses

Low-frequency vibrational harmonic modes of glasses are frequently used to rationalize their universal low-temperature properties. One well studied feature is the excess low-frequency density of states over the Debye model prediction. Here, we examine the system size dependence of the density of states for two-dimensional glasses. For systems of fewer than 100 particles, the density of states scales with the system size as if all the modes were plane-wave-like. However, for systems greater than 100 particles, we find a different system-size scaling of the cumulative density of states below the first transverse sound mode frequency, which can be derived from the assumption that these modes are quasi-localized. Moreover, for systems greater than 100 particles, we find that the cumulative density of states scales with the frequency as a power law with the exponent that leads to the exponent beta = 3.5 for the density of states. For systems whose sizes were investigated, we do not see a size-dependence of exponent beta.

Automated summary

The density of states for two-dimensional glasses exhibits different system-size scaling depending on the number of particles. For systems with fewer than 100 particles, the density of states scales with the system size as if all the modes were plane-wave-like. However, for systems with more than 100 particles, the cumulative density of states below the first transverse sound mode frequency shows a different system-size dependence, suggesting quasi-localized modes. In addition, the cumulative density of states scales with the frequency as a power law with an exponent that leads to β = 3.5 for the density of states.