{
  "abstract": "The exact behaviour of the enveloppes of the single-time and two-time correlators is found for the voter model on a fractal substrate, with nearest-neighbour interactions. Herein the geometry of the fractal substrate is described by its non-integer geometric fractal dimension d f , and its topology and diffusive transport by the distinct spectral dimension d s . On the level of the equations of motion of the correlators this can be modelled by considering a space-dependent diffusion constant D(r) ∼ r -θ which implies the spectral index θ, itself a function of d f and d s . With a scaling ansatz, the generic phenomenology of ageing is confirmed and the dynamic exponent z = 2 + θ and the autocorrelation exponent λ = d f are derived. The explicitly found dynamic scaling functions are shown to depend only on the spectral dimension d s . The decay of the enveloppe of the density of active interfaces with time is described by the exponent α = 1 -d s /2 for d s < 2, confirming the results of preexisting numerical simulations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24408",
  "author_total": 1,
  "authors": [
    {
      "name": "Malte Henkel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0epm6ecat2v8h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24408",
  "fulltext_url": null,
  "id": "0epm6ecat2v8h",
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  "landing_url": "https://hal.science/hal-05757079v1",
  "language": "en",
  "licence": "CC-BY-4.0",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
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      "cond-mat.stat-mech"
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  "openalex": "W7214037901",
  "pdf_url": "https://hal.science/hal-05757079/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0epm6ecat2v8h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:37Z",
      "native_id": "hal-05757079",
      "source": "hal",
      "url": "https://hal.science/hal-05757079v1"
    },
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2609.24408",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24408"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Ageing in the exact correlations of the voter model on a fractal",
  "title_text": "Ageing in the exact correlations of the voter model on a fractal",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/0epm6ecat2v8h",
  "venue": "HAL",
  "versions": []
}