GEOMETRICAL FOLDING TRANSITIONS OF THE TRIANGULAR LATTICE IN THE FACE-CENTERED-CUBIC LATTICE

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 fol ds are complete planar folds, folds with the angle of a regular tetrah edron (71 degrees) or with that of a regular octahedron (109 degrees). We study this model in the presence of a negative bending rigidity K, which favours the folding process. We use both a cluster variation me thod (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 tri angular lattice is preferentially wrapped around octahedra from a phas e where it is preferentially wrapped around tetrahedra. A second conti nuous transition separates this latter phase from a phase of complete folding of the lattice on top of a single triangle. (C) 1997 Elsevier Science B.V.