Tethered surfaces: Statics and dynamics

We apply renormalization-group and Monte Carlo methods to study the equilibrium conformations and dynamics of two-dimensional surfaces of fixed connectivity embedded in d dimensions, as exemplified by hard spheres tethered together by strings into a triangular net. A continuum description of the surfaces is obtained. Without self-avoidance, the radius of gyration increases as √lnL , where L is the linear size of the uncrumpled surface. The upper critical dimension of self-avoiding surfaces is infinite. Their radius of gyration grows as $L^{\nu }$, where Flory theory predicts ν=4/(d+2), in agreement with our Monte Carlo result ν=0.80±0.05 in d=3. The Rouse relaxation time of a self-avoiding surface grows as $L^{3.6}$.