1996/11/13 by Mark J. Bowick, Mark Bowick, O. Golinelli +3 · 2 citations
Engineering · Physics and Astronomy · #Advanced Materials and Mechanics #Micro and Nano Robotics #Theoretical and Computational Physics #cond-mat.stat-mech #hep-th
paper · pdf · doi:10.1016/s0550-3213(97)00198-3
published as Nucl.Phys. B495 (1997) 583-607 · 25 pages, uses harvmac(b) and epsf, 14+1 figures included
arxiv created 1996/11/13 · openalex publication_date 1997/06/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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 phantom membranes. Possible folds are complete planar folds, folds with the angle of a regular tetrahedron (71°) or with that of a regular octahedron (109°). We study this model in the presence of a 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 |K|: 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.