{
  "abstract": "Truncating weak interactions is a natural simplification of a many-body Hamiltonian, but the validity of this approximation need not be uniform in distance and time. In a chaotic system, a weak long-range coupling can seed a small disturbance far from its source, after which the local dynamics can amplify that disturbance exponentially. We study this mechanism in an infinite-temperature classical Heisenberg spin chain with a dominant nearest-neighbor exchange and a weak interaction tail. Using a classical decorrelator, we compare exponentially and power-law decaying tails over several decades in interaction strength. For exponentially decaying interactions, the long-distance front remains ballistic when the tail is sufficiently shallow, with a velocity controlled by the competition between the spatial decay of the seed and the local chaotic growth. For sufficiently rapid exponential decay, the nearest-neighbor front, which is defined by an intrinsic butterfly velocity $v_b$, is recovered within the accessible space-time window. For power-law interactions, the arrival time is logarithmic in distance for all exponents studied, corresponding to an exponentially expanding spatial front; the power-law exponent controls the coefficient of this logarithm. We interpret both behaviors using a seeding-and-amplification picture in which long-range couplings generate weak disturbances throughout the chain whose growth is governed primarily by the local nearest-neighbor dynamics. In this picture, the overall strength of the tail primarily controls when the long-range front becomes visible, while its spatial decay controls the propagation law. Thus a weak interaction tail can leave conventional spin-dynamical observables essentially unchanged while qualitatively altering the long-distance propagation of decorrelation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40417",
  "author_total": 2,
  "authors": [
    {
      "name": "Sareen Sabra"
    },
    {
      "name": "Jeffrey G. Rau"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/37p2g743tw3an.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40417",
  "fulltext_url": null,
  "id": "37p2g743tw3an",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40417",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.stat-mech"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40417",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/37p2g743tw3an.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:28Z",
      "native_id": "2610.40417",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40417"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Seeding and Amplification of Chaos in Long-Range Interacting Spin Chains",
  "title_text": "Seeding and Amplification of Chaos in Long-Range Interacting Spin Chains",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:47Z",
  "url": "https://research.draconitic.com/paper/37p2g743tw3an",
  "venue": "arXiv",
  "versions": []
}