General self-flattening surfaces

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Recently Jeong and Kim [Phys. Rev. E 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≈ 0.561 and the window exponent δ≈ 0.423. We present an analytic argument for general self-flattening surfaces in D dimensions, leading to α=Dα₀ /(D+α₀) and δ=D/(D+α₀) where α₀ 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 α₀=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.