Mermin-Wagner fluctuations in 2D amorphous solids

In a recent comment, M. Kosterlitz described how the discrepancy about the lack of broken translational symmetry in two dimensions - doubting the existence of 2D crystals - and the first computer simulations foretelling 2D crystals at least in tiny systems, motivated him and D. Thouless to investigate melting and suprafluidity in two dimensions [Jour. of Phys. Cond. Matt. \textbf{28}, 481001 (2016)]. The lack of broken symmetries proposed by D. Mermin and H. Wagner is caused by long wavelength density fluctuations. Those fluctuations do not only have structural impact but additionally a dynamical one: They cause the Lindemann criterion to fail in 2D and the mean squared displacement not to be limited. Comparing experimental data from 3D and 2D amorphous solids with 2D crystals we disentangle Mermin-Wagner fluctuations from glassy structural relaxations. Furthermore we can demonstrate with computer simulations the logarithmic increase of displacements predicted by Mermin and Wagner: periodicity is not a requirement for Mermin-Wagner fluctuations which conserve the homogeneity of space on long scales.Comment: 7 pages, 4 figure