Folding of the Triangular Lattice with Quenched Random Bending Rigidity

Abstract

We study the problem of folding of the regular triangular lattice in the presence of a quenched random bending rigidity + or - K and a magnetic field h (conjugate to the local normal vectors to the triangles). The randomness in the bending energy can be understood as arising from a prior marking of the lattice with quenched creases on which folds are favored. We consider three types of quenched randomness: (1) a ``physical'' randomness where the creases arise from some prior random folding; (2) a Mattis-like randomness where creases are domain walls of some quenched spin system; (3) an Edwards-Anderson-like randomness where the bending energy is + or - K at random independently on each bond. The corresponding (K,h) phase diagrams are determined in the hexagon approximation of the cluster variation method. Depending on the type of randomness, the system shows essentially different behaviors.

uses harvmac (l), epsf, 17 figs included, uuencoded, tar compressed

References in corpus (8)

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Cited by in corpus (4)

• Geometrically constrained statistical systems on regular and random lattices: From folding to meanders
• Geometrical Folding Transitions of the Triangular Lattice in the Face-Centred Cubic Lattice
• Exactly solvable flat-foldable quadrilateral origami tilings
• Folding of the Triangular Lattice in the FCC Lattice with Quenched Random Spontaneous Curvature