Publication : t96/124
Geometrical folding transitions of the triangular lattice in the face-centred cubic lattice
Bowick M.J. (Physics Department, Syracuse University, 201 Physics Building, Syracuse, NY 13244-1130, USA)Golinelli O. (CEA, DSM, SPhT (Service de Physique Théorique), F-91191 Gif-sur-Yvette, FRANCE)
Guitter E. (CEA, DSM, SPhT (Service de Physique Théorique), F-91191 Gif-sur-Yvette, FRANCE)
Mori S. (Department of Physics, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033, JAPAN)
Abstract:Année de publication : 1997
We study the folding of the regular two-dimensional triangular lattice embedded in the regular three-dimensional Face-Centred Cubic lattice, a discrete model for the crumpling of membranes. Possible folds are complete planar folds, folds with the angle of a regular tetrahedron ($71^\circ$) or with that of a regular octahedron ($109^\circ$). We study this model in the presence of a {\it negative} bending rigidity $K$, which favours the folding process. We use both a cluster variation method (CVM) approximation and a transfer matrix approach. The system is shown to undergo two separate geometrical transitions with increasing $\vert K\vert$: a first discontinuous transition separates a phase where the triangular lattice is preferentially wrapped around octahedra from a phase where it is preferentially wrapped around tetrahedra. A second continuous transition separates this latter phase from a phase of complete folding of the lattice on top of a single triangle.
Revue : Nucl. Phys. B [FS] 495 583-607 (1997)
DOI : 10.1016/S0550-3213(97)00198-3
Preprint : arXiv:cond-mat/9611105
Langue : Anglais
Fichier(s) à télécharger :
nucl_phys_b-495-583.pdf publi.pdf
