{
  "abstract": "We compare two Markov chain Monte Carlo dynamics for Ising spin glasses with rotationally invariant couplings: the synchronous Monte Carlo method (SyncMC), which updates all spins in parallel with the help of Gaussian auxiliary fields, and asynchronous Metropolis-Hastings dynamics, which updates one spin at a time. Using the Guionnet-Maïda formula, we derive the dynamical mean-field theory of both dynamics in terms of the R-transform of the coupling spectrum. The two effective single-spin processes share a retarded self-interaction and a Gaussian noise; SyncMC has, in addition, an instantaneous self-coupling and a noise that depends only on the response function. These additional terms act only on the fastest time scale, so that the equations for slow time scales, including the fluctuation-dissipation ratio and, for the Sherrington-Kirkpatrick model, the Parisi equation, are the same for the two dynamics. Simulations of the random orthogonal and Sherrington-Kirkpatrick models confirm that both dynamics approach the same fluctuation-dissipation relations, differing only in how many updates they need to do so.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24942",
  "author_total": 1,
  "authors": [
    {
      "name": "Yoshiyuki Kabashima"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1qgs55v927tcy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24942",
  "fulltext_url": null,
  "id": "1qgs55v927tcy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24942",
  "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.dis-nn"
    ],
    [
      "openalex",
      "3104|Theoretical and Computational Physics"
    ]
  ],
  "openalex": "W7223008267",
  "pdf_url": "https://arxiv.org/pdf/2610.24942",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1qgs55v927tcy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2610.24942",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24942"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Synchronous and asynchronous Monte Carlo dynamics of mean-field spin glasses with rotationally invariant couplings: what they share and where they differ",
  "title_text": "Synchronous and asynchronous Monte Carlo dynamics of mean-field spin glasses with rotationally invariant couplings: what they share and where they differ",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/1qgs55v927tcy",
  "venue": "arXiv",
  "versions": []
}