General self-flattening surfaces

Abstract

Recently Jeong and Kim [Phys. Rev. E {\bf 66}, 051605 (2002)] investigated the scaling properties of equilibrium self-flattening surfaces subject to a restricted curvature constraint. In one dimension (1D), they found numerically that the stationary roughness exponent $α\approx 0.561$ and the window exponent $δ\approx 0.423$. We present an analytic argument for general self-flattening surfaces in $D$ dimensions, leading to $α=Dα_0 /(D+α_0)$ and $δ=D/(D+α_0)$ where $α_0$ is the roughness exponent for equilibrium surfaces without the self-flattening mechanism. In case of surfaces subject to a restricted curvature constraint, it is known exactly that $α_0=3/2$ in 1D, which leads to $α=3/5$ and $δ=2/5$. Small discrepancies between our analytic values and their numerical values may be attributed to finite size effects.