Unveiling Dimensionality Dependence of Glassy Dynamics: 2D Infinite Fluctuation Eclipses Inherent Structural Relaxation

TL;DR

This study reveals that 2D supercooled liquids exhibit size-dependent glassy dynamics due to long-wavelength fluctuations, while 3D systems do not, highlighting the transient nature of finite-size effects in 2D.

Contribution

It demonstrates the origin of size dependence in 2D glassy dynamics as stemming from enhanced long-wavelength fluctuations, contrasting with 3D systems where such effects are absent.

Findings

Size dependence in 2D systems is due to long-wavelength fluctuations.

Vibrational density of states aligns with Debye approximation at low wavenumbers.

Structural relaxation is similar in 2D and 3D systems beyond transient effects.

Abstract

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.