{
  "abstract": "We study the zero-temperature random-field Ising model with +-J bond disorder on sparse graphs as a model of an electorate: survey-derived, trimodal fields compete with social couplings, a fraction alpha of which are antagonistic. With exact ground states up to N=180 (over 78000 optimizations, certified except in the densest frustrated cases) and validated heuristics to N=720, we locate the crossover r_h* at which the field carries half of the ground-state energy, close to where half the voters held against their own field have switched (0.93 r_h* for alpha<=0.2). Our main test is a zero-temperature cavity theory solved on the graph ensemble with no fitted parameter: at seven densities not otherwise used, predicted before their exact ground states were computed, it placed r_h* within 10% in 19 of 21 cells (median error 3%). Its errors are unsigned at alpha=0.05 and 0.5 but all negative at alpha=0.2, where it predicts the coupling energy correctly but a crossover that is early and, at high density, too sharp, and where its replica-symmetric solution is unstable in six of seven cells, consistent with replica-symmetry breaking at intermediate frustration. Empirically r_h*~0.91 e_J(0), with e_J(0) the coupling energy of the zero-field ground state, inside a rigorous per-instance factor-of-two window, so the known +-J energy laws carry over: r_h* ~ ^gamma with gamma=1.01-1.09 for alpha=0.05 and 0.50-0.57 for alpha>=0.5 (=3-28; five graph families agree at matched density). At intermediate frustration r_h* is not a power law: sparse networks accommodate antagonistic ties at the cost of cooperative ones, which stops paying near ~10; the theory reproduces this without adjustment. In weakly frustrated dense networks the ground state is a near-consensus following the sign of the aggregate field in 93-100% of realisations at small r_h, against near-chance agreement in frustrated ones.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32021",
  "author_total": 1,
  "authors": [
    {
      "name": "Natalia Romero"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/29hzhe9j47gaz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32021",
  "fulltext_url": null,
  "id": "29hzhe9j47gaz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32021",
  "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"
    ],
    [
      "arxiv",
      "physics.soc-ph"
    ],
    [
      "openalex",
      "3109|Opinion Dynamics and Social Influence"
    ]
  ],
  "openalex": "W7223705509",
  "pdf_url": "https://arxiv.org/pdf/2610.32021",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/29hzhe9j47gaz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:15Z",
      "native_id": "2610.32021",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32021"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.soc-ph",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Conviction versus Conformity in a Random-Field Ising Electorate: Antagonistic Ties, Network Density, and a Parameter-Free Prediction",
  "title_text": "Conviction versus Conformity in a Random-Field Ising Electorate: Antagonistic Ties, Network Density, and a Parameter-Free Prediction",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:15Z",
  "url": "https://research.draconitic.com/paper/29hzhe9j47gaz",
  "venue": "arXiv",
  "versions": []
}