A Spin model for global flat-foldability of random origami

Author:

Chihiro Nakajima

Keyword:

Condensed Matter, Disordered Systems and Neural Networks, Disordered Systems and Neural Networks (cond-mat.dis-nn)

journal:

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date:

2024-03-12 00:00:00

Abstract

We map the problem of determining flat-foldability of the origami diagram onto the ground-state search problem of spin glass model on random graphs. If the origami diagram is locally flat-foldable around each vertex, a pre-folded diagram, showing the planar-positional relationship of the facet, can be obtained. For remaining combinatorial problem on layer ordering of facets can be described as a spin model. A spin variable is assigned for the layer-ordering of each pair of facets which have an overlap in the pre-folded diagram. The interactions to prohibit the intrusion of each facet into the other component of the same origami diagram are introduced among two or four spins. The flat-foldability of the diagram is closely related to the (non-)existence of frustrated loops on the spin model with the interactions on the random (hyper)graph.