Three-dimensional Folding of the Triangular Lattice

Details Three-dimensional Folding of the Triangular Lattice Three-dimensional Folding of the Triangular Lattice

1995-02-15

arxiv.org/abs/cond-mat/9502063v1

Nucl.Phys. B450 (1995) 463-494

Physics

Condensed Matter

55 pages, uuencoded, uses harvmac (l mode) and epsf, 19+2 figures included

Scientific paper

10.1016/0550-3213(95)00290-9

We study the folding of the regular triangular lattice in three dimensional embedding space, a model for the crumpling of polymerised membranes. We consider a discrete model, where folds are either planar or form the angles of a regular octahedron. These "octahedral" folding rules correspond simply to a discretisation of the 3d embedding space as a Face Centred Cubic lattice. The model is shown to be equivalent to a 96--vertex model on the triangular lattice. The folding entropy per triangle ${\rm ln} q_{3d}$ is evaluated numerically to be $q_{3d}=1.43(1)$. Various exact bounds on $q_{3d}$ are derived.

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