We consider the influence of thermal fluctuations on systems with negligible surface tension ("membranes"), whose behavior is determined by curvature effects. Fluctuations change the effective rigidity and other relevant parameters. Two-dimensional membranes appear rigid at short distances and crumpled at long distances. For more than two-dimensional membranes (or in presence of long-range forces) a crumpling transition separates a rigid low-temperature phase from a crumpled high-temperature one.

• Received 4 February 1985

DOI:https://doi.org/10.1103/PhysRevLett.54.1690