J. Phys. I France
Volume 1, Numéro 12, December 1991
Page(s) 1695 - 1708
DOI: 10.1051/jp1:1991237
J. Phys. I France 1 (1991) 1695-1708

Self-avoinding tethered membranes embedded into high dimensions

Gary S. Grest

Corporate Research Science Laboratories, Exxon Research and Engineering Company, Annandale, NJ 0881, U.S.A.

(Received 7 June 1991, accepted 5 September 1991)

The equilibrium structure of self-avoiding two-dimensional tethered membranes embedded in a space of dimension d>2 are studied using molecular dynamics simulations for $3 \leq d \leq 8$. For embedding dimension $d \geq 5$, the membranes crumple while they remain flat for $d \leq 4$. In the crumbled phase, the radius of gyration $R_{\rm g}$ increases as $L^{\nu}$, where L is the linear size of the uncrumpled surface, and $\nu$ is significantly larger than the simple Flory estimate $\nu_{\rm F}=4/(d+2)$. For d=4, the membrane remains flat, even in the presence of site-dilution, indicating that as for d=3, random site-dilution alone is not sufficient to produce crumpling of two-dimensional membranes.

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