Surface deconstruction and roughening in the multiziggurat model of wetting

Abstract

We relate a random surface model appropriate for wetting in three dimensions to first-passage percolation for the planar Ising model. This establishes that the macroscopic drop, sitting on a rectangular substrate in the completely wet phase, adopts the shape of a pitched roof. It also suggests that fluctuations about this mean shape are not logarithmic, but rather have a roughness exponent \ensuremath{\chi}=1/3.