Self-avoinding tethered membranes embedded into high dimensions

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Abstract
The equilibrium structure of self~voiding two-dimensional tethered membranes em- bedded in a space ofdimension d > 2 are studied using molecular dynamics simulations for 3 < d < 8. For embedding dimension d > 5, the membranes crumple while they remain flat for d < 4. In the crumbled phase, the radius of gyration Rg increases as L", where L is the linear size of the uncrum- pled surfhce, and v is significantly larger than the simple Flory estimate vp = 4/(d + 2). For d = 4, the membrane remains flat, even in the presence ofsite-dilution, indicating that as for d = 3, random site-dilution alone is not sufficient to produce crumpling of txvo-dimcnsional membranes.

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