Statistical Mechanics of Tethered Surfaces

Abstract

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 ${R}_{G}$ increases as ${(\mathrm{ln}L)}^{\frac{1}{2}}$, where $L$ is the linear size of the uncrumpled surface. With self-avoidance ${R}_{G}$ grows as ${L}^{\ensuremath{\nu}}$, with $\ensuremath{\nu}=\frac{4}{(d+2)}$ as obtained from a Flory theory and in good agreement with our Monte Carlo results for $d=3$.