J. Phys. I France
Volume 2, Numéro 5, May 1992
Page(s) 663 - 676
DOI: 10.1051/jp1:1992171
J. Phys. I France 2 (1992) 663-676

Edge correlations of fluid and tethered membranes

G. Gompper1 and D.M. Kroll2

1  Sektion Physik der Ludwig-Maximilians-Universität München, Theresienstr. 37, 8000 München 2, Germany
2  AHPCRC, University of Minnesota, 1100 Washington Avenue South, Minneapolis, MN 55415, U.S.A.

(Received 27 December 1991, accepted 22 January 1992)

The fluctuations of fluid and polymerized open membranes near a free edge are studied analytically, and using Monte Carlo simulations and scaling arguments. Its is shown that flat, finite (or semi-infinite) fluid membranes with zero edge energy (line tension) and zero Gaussian curvature energy are unstable with respect to non-planar deformations, even on length scales small compared to the persistence length. The flat phase can, however, be stabilized by either a line tension $\delta$, or by a Gaussian curvature with a saddle-splay modulus $\bar\kappa$ in the range $-4\kappa< \bar \kappa < 0$. At the mean-field level, we find $\zeta_{\parallel}-\zeta_{\perp}=\zeta=1$ for stable membranes when $\sigma=0$, and $\zeta_{\parallel}=0.5$ for a finite line tension, where $\zeta_{\parallel}$ and $\zeta_{\perp}$ characterize the decay of correlations in the directions parallel and perpendicular to the membrane edge, and $\zeta$ is the bulk exponent. For tethered membranes, simulation results and scaling arguments imply $\zeta_{\parallel}=\zeta_{\perp}=\zeta$, with $\zeta =$ 0.70.

© Les Editions de Physique 1992