Folding transition of the triangular lattice in a discrete three--dimensional space

Abstract

A vertex model introduced by M. Bowick, P. Di Francesco, O. Golinelli, and E. Guitter (cond-mat/9502063) describing the folding of the triangular lattice onto the face centered cubic lattice has been studied in the hexagon approximation of the cluster variation method. The model describes the behaviour of a polymerized membrane in a discrete three--dimensional space. We have introduced a curvature energy and a symmetry breaking field and studied the phase diagram of the resulting model. By varying the curvature energy parameter, a first-order transition has been found between a flat and a folded phase for any value of the symmetry breaking field.

11 pages, latex file, 2 postscript figures

References in corpus (5)

• Entropy of Folding of the Triangular Lattice
• Folding Transition of the Triangular Lattice
• On the Crumpling Transition in Crystalline Random Surfaces
• Folding transitions of the triangular lattice with defects
• Three-dimensional Folding of the Triangular Lattice

Cited by in corpus (13)

• The Statistical Mechanics of Membranes
• Geometrically constrained statistical systems on regular and random lattices: From folding to meanders
• Folding of the triangular lattice in a discrete three-dimensional space: Density-matrix-renormalization-group study
• Folding of the Triangular Lattice with Quenched Random Bending Rigidity
• Geometrical Folding Transitions of the Triangular Lattice in the Face-Centred Cubic Lattice
• Crumpling transition of the discrete planar folding in the negative-bending-rigidity regime
• Crumpling transition of the triangular lattice without open edges: effect of a modified folding rule
• Exactly solvable flat-foldable quadrilateral origami tilings
• Folding of the triangular lattice in a discrete three-dimensional space: Crumpling transitions in the negative-bending-rigidity regime
• Folding transitions of the square--diagonal two--dimensional lattice
• Folding of the Triangular Lattice in the FCC Lattice with Quenched Random Spontaneous Curvature
• Driven particle flux through a membrane: Two-scale asymptotics of a diffusion equation with polynomial drift
• Inefficiency of the block approximation in diploid Probabilistic Cellular Automata