Scaling Relations between Correlations in the Liquid-Vapor Interface and the Interface Width

Long-ranged density correlations, varying on the scale of the capillary length Lc, exist in the liquid-vapor interface in a weak gravitational field. A scaling hypothesis, similar to that made near the bulk critical point, predicts that in dimensions $d<3$, the interface width W→∞ as Lc→∞. For $d>3$, W can remain finite provided there is power-law decay of correlations for separations less than Lc. These results are consistent with capillary-wave theory.