{
  "abstract": "Motivated by the conflicting findings in prior studies regarding the nature of the phase transition for the three-dimensional antiferromagnetic $J_1$-$J_2$-$J_3$ Ising model on the cubic lattice with $J_1 = J_2 = J_3 = 1.0$, in this study we conduct a detailed investigation of this model using both Monte Carlo simulations and neural networks (NN). Here $J_1$ and $J_2$ are the intralayer nearest-neighbor and next-nearest-neighbor couplings, respectively, and $J_3$ is the nearest-neighbor interlayer interaction. By investigating the data obtained from much larger lattices than those used in previous studies, we find that the phase transition for $J_1 = J_2 = J_3 = 1.0$ is second order without any ambiguity. Hence we bring a resolution to this debate. Apart from $J_1 = J_2 = J_3 = 1.0$, we study the critical phenomenon associated with $J_2/J_1 = 4/7$ and $J_3 = J_1 = 1.0$ as well. In addition, by employing a dedicated training and testing strategy, our NN computation not only is much more efficient than those utilizing the standard procedures commonly used in the literature, but also requires only a per-mille fraction of the storage capacity needed by a conventional NN calculation when a large linear system size $L$ is considered. The method employed here provides an extremely resource-efficient route for applying NN techniques to study the critical behaviors of higher-dimensional systems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25884",
  "author_total": 4,
  "authors": [
    {
      "name": "Kai-Wei Huang"
    },
    {
      "name": "Chien-Ting Chen"
    },
    {
      "name": "Shang-Wei Li"
    },
    {
      "name": "Fu-Jiun Jiang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9k882mvfrf7rx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25884",
  "fulltext_url": null,
  "id": "9k882mvfrf7rx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25884",
  "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.stat-mech"
    ],
    [
      "openalex",
      "3104|Theoretical and Computational Physics"
    ]
  ],
  "openalex": "W7223010467",
  "pdf_url": "https://arxiv.org/pdf/2610.25884",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9k882mvfrf7rx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2610.25884",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25884"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Phase transitions of the antiferromagnetic $J_1$-$J_2$-$J_3$ Ising model on the cubic lattice",
  "title_text": "Phase transitions of the antiferromagnetic J_1-J_2-J_3 Ising model on the cubic lattice",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:41Z",
  "url": "https://research.draconitic.com/paper/9k882mvfrf7rx",
  "venue": "arXiv",
  "versions": []
}