Table of Contents
Conference Papers in Mathematics
Volume 2013 (2013), Article ID 320718, 7 pages
Conference Paper

Rigorous Study of the Unbinding Transition of Biomembranes and Strings from Morse Potentials

1ENSAM, Moulay Ismail University, P.O. Box 25290, Al Mansour, Meknes 50000, Morocco
2Polymer Physics and Critical Phenomena Laboratory, Sciences Faculty Ben M'sik, P.O. Box 7955, Casablanca 20000, Morocco
3CRMEF, P.O. Box 255, Meknes 50000, Morocco

Received 25 March 2013; Accepted 22 May 2013

Academic Editors: G. S. F. Frederico, N. Martins, D. F. M. Torres, and A. J. Zaslavski

This Conference Paper is based on a presentation given by Mabrouk Benhamou at “The Cape Verde International Days on Mathematics 2013” held from 22 April 2013 to 25 April 2013 in Praia, Cape Verde.

Copyright © 2013 Mabrouk Benhamou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The purpose is an exact study of the unbinding transition from two interacting manifolds (strings or bilayer membranes). These systems have similar scaling behavior, and then it is sufficient to consider only the strings’ problem. We assume that the manifolds interact via a realistic potential of Morse type. To this end, the use is made of the transfer matrix method, based on the resolution of a Schrödinger equation. We first determine the associated bound states and energy spectrum. Second, the exact ground state energy gives the free energy density, from which we extract the expression of the unbinding temperature. Third, we determine the contact probability between manifolds, from which we compute the (diverging) average separation and roughness of the manifolds. It is found that their critical behavior is close to that obtained using Field-Theoretical Renormalization-Group. The conclusion is that these analytical studies reveal that the Morse potential is a good candidate for the study of the unbinding phenomenon within manifolds. Finally, the discussion is extended to generalized Morse potential.