{"title":"A Spin model for global flat-foldability of random origami","authors":"Chihiro Nakajima","doi":"arxiv-2403.07306","DOIUrl":null,"url":null,"abstract":"We map the problem of determining flat-foldability of the origami diagram\nonto the ground-state search problem of spin glass model on random graphs. If\nthe origami diagram is locally flat-foldable around each vertex, a pre-folded\ndiagram, showing the planar-positional relationship of the facet, can be\nobtained. For remaining combinatorial problem on layer ordering of facets can\nbe described as a spin model. A spin variable is assigned for the\nlayer-ordering of each pair of facets which have an overlap in the pre-folded\ndiagram. The interactions to prohibit the intrusion of each facet into the\nother component of the same origami diagram are introduced among two or four\nspins. The flat-foldability of the diagram is closely related to the\n(non-)existence of frustrated loops on the spin model with the interactions on\nthe random (hyper)graph.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"149 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Disordered Systems and Neural Networks","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2403.07306","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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.