Fig. 4.

MSD and CR-MSD of a hard disk system for various system sizes at $\varphi =\mathrm{\hspace{0.17em}0.81}$ for $N=\mathrm{1,000}$ up to 16,000 particles. Although the CR-MSD (blue) does not show finite size effects in the plateau, the standard MSD (red) is strongly affected. Increasing opacity of the curves corresponds to increasing size. A total of $250$ independent simulations were performed for each curve (except for $N=16\text{,}000$ with $191$ runs). Inset shows the linear amplitude of the fluctuations $\sqrt{\mathrm{MSD}({\tau }_i)}$ vs. system size $L\propto \sqrt{N}$ in log-lin scale. ${\tau }_i$ is given by the inflection point of the curves, marked as gray circles. The straight line is a linear fit of the log₁₀(L) behavior and verifies Mermin–Wagner fluctuations in 2D amorphous solids.