The image shows a (quasi-) two-dimensional crystal of colloidal particles. These are micrometre-sized particles dispersed in water and sedimented on a flat interface, thus they can perform Brownian motions only within a plane. The sixfold crystalline order is easy to detect on a local scale, since the logarithmic increase of displacements is rather slow. The deviations from the (red) lattice axis are easy to detect, too, here shown as green arrows. The deviations are basically given by the elastic lattice vibrations (acoustic phonons). A direct experimental proof of Hohenberg–Mermin–Wagner fluctuations would be, if the displacements increase logarithmic with the distance of a locally fitted coordinate frame (blue). This logarithmic divergence goes along with an algebraic (slow) decay of positional correlations. The spatial order of a 2D crystal is called quasi-long-range (see also such hexatic phase for the phase behaviour of 2D ensembles). Interestingly, significant signatures of Hohenberg–Mermin–Wagner fluctuations have not been found in crystals but in disordered amorphous systems.