Phase diagram of randomly polymerized membrane

Using a replica formalism, a generalization of a recent mean field model co rresponding to the observed wrinkling transition in randomly polymerized me mbranes is presented. In this model we study the effects of global fluctuat ions of the surface normals to the flat membrane, which can be introduced b y a random local field. In absence of these global fluctuations, we show th at, the model exhibits both continuous and discontinuous transitions betwee n flat and wrinkled phases, contrary to what has been predicted by Bensimon et al. and Attal et al. Phase diagrams both in replica symmetry and in bre aking of replica symmetry in sense of Almeida and Thouless are given. We ha ve also investigated the effects of global fluctuations on the replica symm etry phase diagram. We show that, the wrinkled phase is favored and the fla t phase is unstable. For large global fluctuations, the transition between wrinkled and flat phases becomes first order.