Geometrical Folding Transitions of the Triangular Lattice in the Face-Centred Cubic Lattice
arXiv:cond-mat/9611105 · doi:10.1016/S0550-3213(97)00198-3
Abstract
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 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 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.
25 pages, uses harvmac(b) and epsf, 14+1 figures included
References in corpus (6)
- Entropy of Folding of the Triangular Lattice
- Folding Transition of the Triangular Lattice
- Folding transitions of the triangular lattice with defects
- Three-dimensional Folding of the Triangular Lattice
- Folding transition of the triangular lattice in a discrete three--dimensional space
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Cited by in corpus (9)
- The Statistical Mechanics of Membranes
- Geometrically constrained statistical systems on regular and random lattices: From folding to meanders
- Folding of the triangular lattice in a discrete three-dimensional space: Density-matrix-renormalization-group study
- Crumpling transition of the discrete planar folding in the negative-bending-rigidity regime
- Exactly solvable flat-foldable quadrilateral origami tilings
- Crumpling transition of the triangular lattice without open edges: effect of a modified folding rule
- Folding of the triangular lattice in a discrete three-dimensional space: Crumpling transitions in the negative-bending-rigidity regime
- Folding transitions of the square--diagonal two--dimensional lattice
- Folding of the Triangular Lattice in the FCC Lattice with Quenched Random Spontaneous Curvature