Three-dimensional folding of the triangular lattice

M. Bowick; P. Di Francesco; O. Golinelli; E. Guitter

doi:10.1016/0550-3213(95)00290-9

Three-dimensional folding of the triangular lattice

M. Bowick, P. Di Francesco, O. Golinelli, E. Guitter

Department of Physics

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23 Scopus citations

Abstract

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 ln q_3d is evaluated numerically to be q_3d = 1.43(1). Various exact bounds on q_3d are derived.

Original language	English (US)
Pages (from-to)	463-494
Number of pages	32
Journal	Nuclear Physics, Section B
Volume	450
Issue number	3
DOIs	https://doi.org/10.1016/0550-3213(95)00290-9
State	Published - Sep 18 1995

ASJC Scopus subject areas

Nuclear and High Energy Physics

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10.1016/0550-3213(95)00290-9

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title = "Three-dimensional folding of the triangular lattice",

abstract = "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 ln q3d is evaluated numerically to be q3d = 1.43(1). Various exact bounds on q3d are derived.",

author = "M. Bowick and {Di Francesco}, P. and O. Golinelli and E. Guitter",

note = "Funding Information: The research of M.B. was supported by the Department of Energy, USA, under contract No. DE-FG02-85ER40237. M.B. and E.G. are also grateful for support under NSF grant No. PHY89-04035 from the Institute for Theoretical Physics at Santa Barbara, where this work was initiated. We thank J.-M. Normand for a critical reading of the manuscript.",

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AU - Di Francesco, P.

AU - Golinelli, O.

AU - Guitter, E.

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PY - 1995/9/18

Y1 - 1995/9/18

N2 - 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 ln q3d is evaluated numerically to be q3d = 1.43(1). Various exact bounds on q3d are derived.

AB - 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 ln q3d is evaluated numerically to be q3d = 1.43(1). Various exact bounds on q3d are derived.

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JO - Nuclear Physics B

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Three-dimensional folding of the triangular lattice

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