{
  "abstract": "We identify the limit free energy of all multi-species spin glasses with centered ±1 spins. The result was previously known only under a convexity assumption on the covariance function of the Hamiltonian. We also obtain a one-species reduction of the formula for balanced multi-species models.",
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  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.16636",
  "author_total": 3,
  "authors": [
    {
      "name": "Hong-Bin Chen"
    },
    {
      "name": "Victor Issa"
    },
    {
      "name": "Jean-Christophe Mourrat"
    }
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  "bibtex": "https://research.draconitic.com/paper/cq1qvptjjhtr9.bib",
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  "doi": "10.48550/arxiv.2606.16636",
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  "id": "cq1qvptjjhtr9",
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  "pdf_url": "https://hal.science/hal-05777136/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cq1qvptjjhtr9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:47Z",
      "native_id": "hal-05777136",
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      "url": "https://hal.science/hal-05777136v1"
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      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2606.16636",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.16636"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
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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 spin glasses with centered Ising spins",
  "title_text": "Free energy of non-convex multi-species spin glasses with centered Ising spins",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/cq1qvptjjhtr9",
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}