Statistical Mechanics of Tethered Surfaces

We study the statistical mechanics of two-dimensional surfaces of fixed connectivity embedded in d dimensions, as exemplified by hard spheres tethered together by strings into a triangular net. Without self-avoidance, entropy generates elastic interactions at large distances, and the radius of gyration RG increases as (lnL)1/2, where L is the linear size of the uncrumpled surface. With self-avoidance RG grows as L^ν, with ν=4/(d+2) as obtained from a Flory theory and in good agreement with our Monte Carlo results for $d=3$.