### 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 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.

Original language | English (US) |
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Pages (from-to) | 583-607 |

Number of pages | 25 |

Journal | Nuclear Physics B |

Volume | 495 |

Issue number | 3 |

DOIs | |

State | Published - Jun 30 1997 |

### Keywords

- Bending rigidity
- Crumpling
- Folding
- Membrane
- Phase transition

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

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## Cite this

*Nuclear Physics B*,

*495*(3), 583-607. https://doi.org/10.1016/S0550-3213(97)00198-3