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Geometrical Folding Transitions of the Triangular Lattice in the Face-Centred Cubic Lattice

Mark Bowick·Olivier Golinelli·Emmanuel Guitter·Shintaro Mori
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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.

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Mark Bowick, Olivier Golinelli, Emmanuel Guitter, Shintaro Mori. 1996-11-13. Geometrical Folding Transitions of the Triangular Lattice in the Face-Centred Cubic Lattice. https://doi.org/10.1016/s0550-3213(97)00198-3

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