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 χ=1/3.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics