Self-avoinding tethered membranes embedded into high dimensions

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 ≤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 Lν, where L is the linear size of the uncrumpled surface, and ν is significantly larger than the simple Flory estimate νF=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.