Vanishing tension of fluctuating membranes

(Received 3 January 1991, revised 5 April 1991, accepted 19 April 1991)

Abstract
The statistical behavior of fluctuating, flexible membranes or films can be governed by their (surface) tension or by their curvature energy, depending on imposed boundary conditions. We present here simple thermodynamic arguments which enable us to classify the different physical situations. In particular, we clarify the notion of vanishing tension, and the (or some of the) conditions under which it can occur. Then, in view of this classification, we reconsider the effects of thermal fluctuations on tension and rigidity, and briefly discuss the experimental systems in which renormalization effects should be expected and could be observed.