J. Phys. I France 2 (1992) 663-676
Edge correlations of fluid and tethered membranesG. 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 , or by a Gaussian curvature with a saddle-splay modulus in the range . At the mean-field level, we find for stable membranes when , and for a finite line tension, where and characterize the decay of correlations in the directions parallel and perpendicular to the membrane edge, and is the bulk exponent. For tethered membranes, simulation results and scaling arguments imply , with 0.70.
© Les Editions de Physique 1992