{
  "abstract": "We identify the limit free energy of all mean-field multi-species spin glasses defined on products of spheres. In particular, we do not make any convexity assumption on the covariance function of the Hamiltonian, and we allow for the presence of external fields. We also obtain a one-species reduction of the formula in the special case of balanced models.",
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  "article_type": null,
  "arxiv": "2609.32710",
  "author_total": 2,
  "authors": [
    {
      "name": "Hong-Bin Chen"
    },
    {
      "name": "Jean-Christophe Mourrat"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bsb03f79n7ja7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32710",
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  "id": "bsb03f79n7ja7",
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  "landing_url": "https://hal.science/hal-05777144v1",
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  "licence": "CC-BY-4.0",
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  "pdf_url": "https://hal.science/hal-05777144/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bsb03f79n7ja7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:47Z",
      "native_id": "hal-05777144",
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      "url": "https://hal.science/hal-05777144v1"
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      "native_id": "2609.32710",
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      "url": "https://arxiv.org/abs/2609.32710"
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    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
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    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
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  "title": "Free energy of non-convex multi-species spherical spin glasses",
  "title_text": "Free energy of non-convex multi-species spherical spin glasses",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/bsb03f79n7ja7",
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}