{
  "abstract": "We investigate the non-equilibrium phase transitions of the continuous-trait Axelrod model, an agent-based framework where individual culture is represented by a vector of $F$ continuous features confined to the interval $(0,1)$. Local interactions are governed by a metric similarity threshold $d$, which acts as a continuous control parameter of social tolerance. The dynamics inevitably freeze into one of two absorbing configuration classes: an ordered, homogeneous monocultural state at high tolerance, or a highly fragmented, disordered state at low tolerance. While previous studies characterized the transition as hybrid based on the continuous behavior of the domain density $μ$ alongside a discontinuous jump in the largest domain fraction $ρ$, we show that this apparent continuity is an artifact of severe finite-size masking effects. By shifting the methodological focus to the scaling of the median $\\tildeμ$ and analyzing the full probability distributions $P(μ)$, we unveil a clear bimodal structure with disjoint maxima across independent simulation runs. Our results reveal that for $F=2$, the system undergoes a genuinely hybrid transition in the contemporary sense, featuring a tiny but finite latent jump ($μ_c \\approx 0.089$) at the critical threshold $d_c \\approx 0.0784$ while scaling toward it from below via a non-analytical power law with a mean-field exponent $β\\approx 1/2$. Conversely, for $F=3$, the higher trait-space dimensionality suppresses local fluctuations, yielding a traditional, non-hybrid first-order transition. We apply this framework to the alternative discrete Poisson variant of the model, successfully confirming its known continuous transition for $F=2$ and discontinuous, non-hybrid transition for $F=3$, thereby establishing a unified characterization of phase transitions in Axelrod-like systems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: J. Stat. Mech. (2026) 093404",
  "arxiv": "2607.10381",
  "author_total": 3,
  "authors": [
    {
      "name": "Sandro M. Reia"
    },
    {
      "name": "Paulo R. A. Campos"
    },
    {
      "name": "José F. Fontanari"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5dr8yjd2nd15w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.10381",
  "fulltext_url": null,
  "id": "5dr8yjd2nd15w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.10381",
  "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"
    ],
    [
      "arxiv",
      "nlin.AO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2607.10381",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5dr8yjd2nd15w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2607.10381",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.10381"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Revisiting the non-equilibrium phase transitions of the continuous-trait Axelrod model",
  "title_text": "Revisiting the non-equilibrium phase transitions of the continuous-trait Axelrod model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:12Z",
  "url": "https://research.draconitic.com/paper/5dr8yjd2nd15w",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1088/1742-5468/aea553",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}