{
  "abstract": "We find no evidence of critical scaling in the Schelling segregation model, in either the Moore neighborhood or its dense-spectrum extension to Chebyshev radii up to $r_0 = 6$ ($k = 168$ neighbors). On periodic grids up to $L = 320$ with 50 trials per point (> 12,500 runs), every finite-size scaling diagnostic in the Moore baseline fails: the per-$L$ $T_c$ does not drift, Var$(S) \\sim L^{-2.02 \\pm 0.09}$ matches trivial averaging, $γ/ν\\approx 0$, and the scaling collapse never reaches a finite optimum. The 8-site Moore neighborhood restricts satisfaction to ratios $j/k$ with $k \\leq 8$, giving $S(T)$ a staircase structure with 23 rational thresholds; discreteness alone does not forbid criticality (cf. the Ising model), but the scaling evidence rules it out empirically. A branching-ratio calculation predicts subcritical cascades of mean size $1/(1-R)$ and is validated by perturbation experiments to within 15%; the multiscalar dissimilarity length stays finite across the transition. The dense-spectrum extension strengthens the negative verdict: across $r_0 \\in {3,4,5,6}$ on $L \\in {40,80,160}$ the Binder cumulant has no $L$-curve crossing and the per-$L$ $T_c$ drift is monotonic and unsaturated; at $r_0 = 4$, extending to $L = 320$ gives $α= -2.70$, below the critical boundary $α= -2$, dissolving an apparent $α= +0.81$ signal visible only on $L \\in {40,80}$. The mechanism is the absence of long-range correlation in equilibrium plus deterministic high-$k$ dynamics, not the staircase structure. With a Beta-distributed heterogeneous tolerance, the intolerant tail drives segregation even at moderate population-average tolerance. The staircase theorem and cascade mechanism together account for the Schelling transition without invoking critical phenomena.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.16557",
  "author_total": 1,
  "authors": [
    {
      "name": "Mouhssine Rifaki"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/88qwwe83hs76s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.16557",
  "fulltext_url": null,
  "id": "88qwwe83hs76s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.16557",
  "language": null,
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  "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",
      "cs.GT"
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      "arxiv",
      "cs.MA"
    ],
    [
      "openalex",
      "3104|Theoretical and Computational Physics"
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  "openalex": "W7203727121",
  "pdf_url": "https://arxiv.org/pdf/2608.16557",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/88qwwe83hs76s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "2608.16557",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.16557"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Absence of critical scaling in the Schelling segregation model",
  "title_text": "Absence of critical scaling in the Schelling segregation model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:41Z",
  "url": "https://research.draconitic.com/paper/88qwwe83hs76s",
  "venue": "arXiv",
  "versions": []
}