Eur. Phys. J. B 6, 503-510 (1998)
https://doi.org/10.1007/s100510050577

Phase diagram of randomly polymerized membrane

¹ Laboratoire de Magnétisme et Physique des Hautes Énergies, Département de Physique, Faculté des Sciences, B.P. 1014, Rabat, Morocco
² Dipartimento di Scienze Fisiche, Università Federico II Mostra d'Oltremare, Pad. 19, 80125 Napoli, Italy

Corresponding author: ^a benyous@fsr.ac.ma

Received: 3 December 1997
Revised: 31 March 1998
Accepted: 3 August 1998
Published online: 15 December 1998

Abstract

Using a replica formalism, a generalization of a recent mean field model corresponding to the observed wrinkling transition in randomly polymerized membranes is presented. In this model we study the effects of global fluctuations of the surface normals to the flat membrane, which can be introduced by a random local field. In absence of these global fluctuations, we show that, the model exhibits both continuous and discontinuous transitions between 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 breaking of replica symmetry in sense of Almeida and Thouless are given. We have also investigated the effects of global fluctuations on the replica symmetry phase diagram. We show that, the wrinkled phase is favored and the flat phase is unstable. For large global fluctuations, the transition between wrinkled and flat phases becomes first order.