{
  "abstract": "We present a closed theory, exact in the $N\\to\\infty$ limit, of the equilibrium spin correlations of the Sherrington--Kirkpatrick spin-glass model evolving with Glauber dynamics, above and at the transition temperature $T_c$. The derivation uses a dynamic cavity approach: in the evolution equation for the selected spin the other spins are represented by a fluctuating field. The influence of the selected spin on this field is included at the linear response level; it is given as a sum of the spin's past flips weighted by the correlations of the unperturbed fluctuating field. The self-consistency condition relates the time-dependent correlations of the selected spin and those of the fluctuating field. The theory predicts a $(T-T_c)^{-2}$ divergence of the relaxation time upon approaching the transition and an $At^{-1/2}$ decay of spin correlations at $T_c$. A numerical solution of the theory gives the amplitude, $A=0.964\\pm 0.007$. The theoretical predictions are in excellent agreement with Glauber dynamics computer simulations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04078",
  "author_total": 1,
  "authors": [
    {
      "name": "Grzegorz Szamel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8z9xvnecge16z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04078",
  "fulltext_url": null,
  "id": "8z9xvnecge16z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04078",
  "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",
      "cond-mat.dis-nn"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04078",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8z9xvnecge16z.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:25Z",
      "native_id": "2611.04078",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04078"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Glauber dynamics of the Sherrington--Kirkpatrick spin-glass model: a dynamical cavity method",
  "title_text": "Glauber dynamics of the Sherrington--Kirkpatrick spin-glass model: a dynamical cavity method",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/8z9xvnecge16z",
  "venue": "arXiv",
  "versions": []
}