We determine the asymptotic behavior of the orientationally averaged structure factor S(q) for a large, flat membrane characterized by a roughness exponent ζ. We show that S(q)∼1/${\mathit{q}}^2$ for q≪1/l, where l is controlled by the amplitude for transverse or longitudinal fluctuations. If l is much larger than the intermonomer distance a and 1/l≪q≪1/a, then S(q)∼1/${\mathit{q}}^{3\mathrm{-}\mathrm{\zeta }}$ or S(q)∼1/${\mathit{q}}^{4/\mathrm{\zeta }\mathrm{-}2}$ for a small or large amplitude for longitudinal fluctuations, respectively. We also consider the case where the surface is self-affine only at large distances.

• Received 31 July 1992

DOI:https://doi.org/10.1103/PhysRevA.46.R6170