BENDING RIGIDITY OF FLUCTUATING MEMBRANES

lattice model of random surfaces is studied including configurations w ith arbitrary topologies, overhangs and bubbles. The Hamiltonian of th e surface includes a term proportional to its area and a scale-invaria nt integral of the squared mean curvature. We propose a discretization of the curvature which ensures the scale-invariance of the bending en ergy on the lattice. Nonperturbative renormalization groups for the su rface tension and the bending rigidity are applied, which are also val id at high temperatures and scales above the persistence length. We fi nd at vanishing surface tensions a closed expression for the scale dep endent rigidity including the usual logarithmic decay at low temperatu res. Different scaling behaviours at non-vanishing tensions occur yiel ding characteristic length scales, which determine the structure of ho mogeneous droplet, lamellar, and microemulsion phases.