Self-Consistent Theory of Polymerized Membranes

Details Self-Consistent Theory of Polymerized Membranes Self-Consistent Theory of Polymerized Membranes

1992-08-27

arxiv.org/abs/cond-mat/9208023v1

Phys.Rev.Lett.69:1209,1992

Physics

Condensed Matter

12 pages, Latex, figures available on request, radz@cmts.harvard.edu

Scientific paper

10.1103/PhysRevLett.69.1209

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 $D_{lc}(d)={2 d \over {d+1}}$ ($D_{lc}={\sqrt{2}}$ for codimension 1). For physical membranes with ${\it random}$ quenched curvature $\zeta=0.775$ in the new $T=0$ flat phase in good agreement with simulations.

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