SELF-CONSISTENT THEORY OF POLYMERIZED MEMBRANES

We study D-dimensional polymerized membranes embedded in d dimensions using a self-consistent screening approximation. It is exact for large d to order l/d, for any d to order epsilon=4-D, and for d=D. For flat physical membranes (D=2, d=3) it predicts a roughness exponent zeta=0.590. For phantom membranes at the crumpling transition the size exponent is v-0.732. It yields identical lower critical dimension for the flat phase and crumpling transition D(lc)(d)=2d/(d + 1) (D(lc)=square-root 2 for codimension 1). For physical membranes with random quenched curvature zeta=0.775 in the new T=0 flat phase in good agreement with simulations.