{
  "abstract": "We study finite-step replica symmetry breaking (RSB) in mixed $p$-spin Ising spin glasses at positive temperature and zero external field. For every integer $k\\geq1$, we construct polynomial mixtures whose Parisi measures are exactly $k$-RSB, with each such phase persisting on an open set of coefficients. More generally, for a broad class of polynomial covariances with an $r$-RSB Parisi measure, adding the interaction term $λq^p$ for sufficiently large even $p$ produces a unique $r$-RSB-to-$(r+1)$-RSB transition as $λ$ varies near a critical value. Since such covariances exist for every $r\\geq0$, this yields transitions of arbitrary depth. The main idea of the proof is that, for large $p$, the perturbation $λq^p$ is negligible for overlaps bounded away from $1$, while its effect is concentrated at overlaps very close to $1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05317",
  "author_total": 2,
  "authors": [
    {
      "name": "P. M. Aronow"
    },
    {
      "name": "Patrick Lopatto"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3thhfamfb5x1z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05317",
  "fulltext_url": null,
  "id": "3thhfamfb5x1z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05317",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "3104|Theoretical and Computational Physics"
    ]
  ],
  "openalex": "W7211872426",
  "pdf_url": "https://arxiv.org/pdf/2609.05317",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3thhfamfb5x1z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2609.05317",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05317"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Replica symmetry breaking at arbitrary depth",
  "title_text": "Replica symmetry breaking at arbitrary depth",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/3thhfamfb5x1z",
  "venue": "arXiv",
  "versions": []
}