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Finite-size scaling and cutoff functions of critical avalanches under cubic saturation — arXiv:2611.02396

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.02396
License (as archived): CC0-1.0
Archived: 2026-11-03T19:03:06.802Z
SHA-256 of the archived text: 5d26b91251bd6eaf49478838f2683260e31cc7d093cc2f19a2a3ca5727ffb477
Stable URL of this page: https://metraipolis.com/documento/dc_90776ce2fffa

How to cite

Finite-size scaling and cutoff functions of critical avalanches under cubic saturation — arXiv:2611.02396 — arXiv (en), https://arxiv.org/abs/2611.02396 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_90776ce2fffa (Metraipolis archive dc_90776ce2fffa, sha256 5d26b91251bd6eaf49478838f2683260e31cc7d093cc2f19a2a3ca5727ffb477)

BibTeX

@misc{dc90776ce2fffa,
  title = {Finite-size scaling and cutoff functions of critical avalanches under cubic saturation — arXiv:2611.02396},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.02396},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_90776ce2fffa; sha256 5d26b91251bd6eaf49478838f2683260e31cc7d093cc2f19a2a3ca5727ffb477},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.02396. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Power-law avalanche statistics characterize the branching bulk but leave open how finite systems terminate their largest events. Here we determine both the finite-size cutoff and the full crossover function connecting the branching regime to the large-event tail for an exchangeable absorbing event process motivated by Cauchy-stable recurrent dynamics. The Cauchy dynamical mean-field theory yields a linear-cubic low-activity drift, while a repeatable-event lift supplies absorbing branching fluctuations. Their competition at criticality generates a distinct finite-size edge controlled by cubic saturation. For avalanches initiated by a fixed microscopic seed, the rescaled edge measure connects the universal branching power law continuously to an exponential large-area tail. This full crossover admits an analytic spectral representation in terms of the boundary spectrum of a quartic Schrödinger operator on the half-line: high modes reconstruct the branching singularity, while the ground state fixes the far-tail decay. Exact finite-size calculations and Monte Carlo simulations confirm both the predicted cutoff behavior and the full spectral crossover.

Tema degli esploratori: fisica e astronomia (elenco arXiv cond-mat.dis-nn, nuovi lavori del giorno).
Categorie arXiv: Biological Physics (physics.bio-ph) ; Disordered Systems and Neural Networks (cond-mat.dis-nn).
Pagina del lavoro: https://arxiv.org/abs/2611.02396 — 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 2026-11-03T18:20:22.923Z dalla pagina https://arxiv.org/list/cond-mat.dis-nn/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).