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Absence of critical scaling in the Schelling segregation model — arXiv:2608.16557

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.16557
License (as archived): CC0-1.0
Archived: 2026-10-18T19:08:10.253Z
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Absence of critical scaling in the Schelling segregation model — arXiv:2608.16557 — arXiv (en), https://arxiv.org/abs/2608.16557 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_f47b036feded (Metraipolis archive dc_f47b036feded, sha256 6b5c09906389fb80df34fb3da8643c347796a831ce0911da82511ab0ef6b24a8)

BibTeX

@misc{dcf47b036feded,
  title = {Absence of critical scaling in the Schelling segregation model — arXiv:2608.16557},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.16557},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_f47b036feded; sha256 6b5c09906389fb80df34fb3da8643c347796a831ce0911da82511ab0ef6b24a8},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.16557. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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, $\gamma/\nu \approx 0$, 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 $\alpha = -2.70$, below the critical boundary $\alpha = -2$, dissolving an apparent $\alpha = +0.81$ 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.

Tema degli esploratori: economia dei servizi IA (retro-catalogo arXiv: annunci del 2026-08-18 in cs.GT).
Categorie arXiv: Statistical Mechanics (cond-mat.stat-mech) ; Computer Science and Game Theory (cs.GT); Multiagent Systems (cs.MA).
Pagina del lavoro: https://arxiv.org/abs/2608.16557 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-18T18:12:50.761Z dalla pagina https://arxiv.org/catchup/cs.GT/2026-08-18?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).