A renormalization group analysis of lattice models of two-dimensional membranes

We study lattice models of two-dimensional membranes of interest in statistical physics. The energy functional of a membrane is expressed as a sum of terms proportional to the surface area of the membrane, an extrinsic curvature and an intrinsic curvature quantity, respectively, but we neglect excluded volume effects. We introduce a renormalization transformation for these models which preserves the form of the energy functional, up to nonlocal terms. Our renormalization group construction is used to analyze the phase diagram and the different critical regimes of our models. We find evidence for a crumpling transition, separating a regime where surfaces are crystalline from one where the surfaces collapse to branched polymers, and we find a third genuine random-surface regime.