title: Mermin-Wagner fluctuations in 2D amorphous solids.
abstract: In a recent commentary, J. M. Kosterlitz described how D. Thouless and he got motivated to investigate melting and suprafluidity in two dimensions [Kosterlitz JM (2016)J Phys Condens Matter28:481001]. It was due to 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). 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 in the sense that the mean squared displacement of atoms is not limited. Comparing experimental data from 3D and 2D amorphous solids with 2D crystals, we disentangle Mermin-Wagner fluctuations from glassy structural relaxations. Furthermore, we demonstrate with computer simulations the logarithmic increase of displacements with system size: Periodicity is not a requirement for Mermin-Wagner fluctuations, which conserve the homogeneity of space on long scales.
authors.affiliation: Department of Physics, University of Konstanz, Konstanz 78464, Germany.
authors.forename: Bernd
authors.initials: B
authors.lastname: Illing
authors.affiliation: Department of Physics, University of Konstanz, Konstanz 78464, Germany.
authors.forename: Sebastian
authors.initials: S
authors.lastname: Fritschi
authors.affiliation: Department of Physics, University of Konstanz, Konstanz 78464, Germany.
authors.forename: Herbert
authors.initials: H
authors.lastname: Kaiser
authors.affiliation: Department of Physics, University of Konstanz, Konstanz 78464, Germany.
authors.forename: Christian L
authors.initials: CL
authors.lastname: Klix
authors.affiliation: Department of Physics, University of Konstanz, Konstanz 78464, Germany.
authors.forename: Georg
authors.initials: G
authors.lastname: Maret
authors.affiliation: Department of Physics, University of Konstanz, Konstanz 78464, Germany Peter.Keim@uni-konstanz.de.
authors.forename: Peter
authors.initials: P
authors.lastname: Keim
keywords: 2D ensembles; Mermin–Wagner fluctuations; confined geometry; glass transition; phase transition