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

Abstract

Long-ranged density correlations, varying on the scale of the capillary length $L_c$, 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 $d<\mathrm{}3\mathrm{}$, the interface width $W\to \infty$ as $L_c\to \infty$. For $d>\mathrm{}3\mathrm{}$, $W$ can remain finite provided there is power-law decay of correlations for separations less than $L_c$. These results are consistent with capillary-wave theory.