Structure and scaling laws of liquid/vapor interfaces close to the critical point

To reach a deeper understanding of fluid interfaces it is necessary to identify a meaningful coarse-graining length that separates intrinsic fluctuations from capillary ones, given the lack of a proper statistical mechanical definition of the latter. Here, with the help of unsupervised learning techniques, we introduce a new length scale based on the local density of the fluid. This length scale follows a scaling law that diverges more mildly than the bulk correlation length upon approaching the critical point. This allows to distinguish regimes of correlated and uncorrelated capillary waves from that of intrinsic fluctuations.