  By using large-scale molecular dynamics simulations, the dynamics of
two-dimensional (2D) supercooled liquids turns out to be dependent on the
system size, while the size dependence is not pronounced in three dimensional
(3D) systems. It is demonstrated that the strong system-size effect in 2D
amorphous systems originates from the enhanced fluctuations at long
wavelengths, which are similar to those of 2D crystal phonons. This observation
is further supported by the frequency dependence of the vibrational density of
states, consisting of the Debye approximation in the low-wavenumber-limit.
However, the system-size effect in the intermediate scattering function becomes
negligible when the length scale is larger than the vibrational amplitude. This
suggests that the finite-size effect in a 2D system is transient and also that
the structural relaxation itself is not fundamentally different from that in a
3D system. In fact, the dynamic correlation lengths estimated from the
bond-breakage function, which do not suffer from those enhanced fluctuations,
are not size dependent in either 2D or 3D systems.
