{
  "abstract": "Higher-order networks take group interactions as given. I ask what happens when a group interaction is made by pairwise dynamics on a graph, and follow it through the transition that decides whether it matters at large scale, Anderson localisation. An emergent hyperedge is a $k$-body bound state of a Hamiltonian whose terms live on the vertices and edges of the graph, Borromean when none of its $(k-1)$-body faces is bound, detected on a finite graph by a $k$-fold coincidence that survives the thermodynamic limit while the $(k-1)$-fold ones vanish. Sparse random graphs produce one from the simplest pairwise dynamics: three distinguishable particles with on-site attraction $U$ and hopping $t$ bind into a trimer before any pair binds. The thresholds are obtained on the Bethe lattice, in closed form for the pair, in both sectors that an expander graph has and a lattice lacks, the one a condensate sees and the one a Fermi liquid sees. On a disordered graph the emergent hyperedges nucleate on rare deep sites and localise before their parts: the compact trimer, with a narrow band and a threefold sensitivity to site energies, undergoes the Anderson transition at a disorder of $1.6t$, against $17t$ for a single particle and $4t$ for a pair, and the Fermi liquid of trimers is a glass above a line between $1.5t$ and $1.7t$, where a liquid of single particles at the same density needs $15t$ to $16t$. The transition is the single-particle cavity transition with the composite's hopping and effective disorder. A group interaction made by pairwise dynamics is an order of magnitude more fragile to heterogeneity than the network that makes it.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32768",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexei Vazquez"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9xhd35ry1d9dy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32768",
  "fulltext_url": null,
  "id": "9xhd35ry1d9dy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32768",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.dis-nn"
    ],
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "physics.soc-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7214701675",
  "pdf_url": "https://arxiv.org/pdf/2609.32768",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9xhd35ry1d9dy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2609.32768",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32768"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Trimers, pairs and localisation on disordered random graphs",
  "title_text": "Trimers, pairs and localisation on disordered random graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:12Z",
  "url": "https://research.draconitic.com/paper/9xhd35ry1d9dy",
  "venue": "arXiv",
  "versions": []
}