Self-Consistent Theory of Polymerized Membranes

Abstract

We study $D$-dimensional polymerized membranes embedded in $d$ dimensions using a self-consistent screening approximation. It is exact for large $d$ to order $1/d$, 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 $\nu =0.732$. It yields identical lower critical dimension for the flat phase and crumpling transition $D_{lc}(d)=\frac{2d}{d+1}$ ($D_{lc}=\sqrt{2}$ 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.

12 pages, Latex, figures available on request, [email protected]

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