Elastic anisotropies and long-ranged interactions in solid membranes

I study the effects of elastic anisotropy and long-ranged interactions on the fluctuations of solid membranes. Elastic anisotropies prove to be irrelevant in the absence of long-ranged interactions. Long-ranged interactions which fall off with distance r like are relevant only for sufficiently small. In real (two-dimensional) membranes with dipolar interactions, the Lamé coefficients and vanish like [ln(1q)]-1, as wave vector. For larger but still relevant exactly, for D-dimensional membranes. © 1989 The American Physical Society.