Self-avoinding tethered membranes embedded into high dimensions

(Received 7 June 1991, accepted 5 September 1991)

Abstract
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 . For embedding dimension , the membranes crumple while they remain flat for . In the crumbled phase, the radius of gyration increases as , where L is the linear size of the uncrumpled surface, and is significantly larger than the simple Flory estimate . 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.