Tethered surfaces: Statics and dynamics

Abstract

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 \ensuremath{\surd}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 ${L}^{\ensuremath{\nu}}$, where Flory theory predicts \ensuremath{\nu}=4/(d+2), in agreement with our Monte Carlo result \ensuremath{\nu}=0.80\ifmmode\pm\else\textpm\fi{}0.05 in d=3. The Rouse relaxation time of a self-avoiding surface grows as ${L}^{3.6}$.