Models of folding of a triangular lattice embedded in a discrete space are studied as simple models of the crumpling transition of fixed-connectivity membranes. Both the case of planar folding and three-dimensional folding on a face-centered-cubic lattice are treated. The 3d-folding problem corresponds to a 96-vertex model and exhibits a first-order folding transition from a crumpled phase to a completely flat phase as the bending rigidity increases.
Bowick, Mark; Francesco, Philippe Di; Golinelli, Oliver; and Guitter, Emmanuel, "Discrete Folding" (1996). Physics - All Scholarship. 168.
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