Finite-size scaling and cutoff functions of critical avalanches under cubic saturation
Abstract
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.
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BibTeX
@misc{kojima2026finitesize,
title = {{Finite-size scaling and cutoff functions of critical avalanches under cubic saturation}},
author = {Ryota Kojima and Kazufumi Hosoda and Hiroyuki Suto and Hitoshi Yamada},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02396},
eprint = {2611.02396},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02396},
}
RIS
TY - UNPB
TI - Finite-size scaling and cutoff functions of critical avalanches under cubic saturation
AU - Ryota Kojima
AU - Kazufumi Hosoda
AU - Hiroyuki Suto
AU - Hitoshi Yamada
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.02396
UR - https://arxiv.org/abs/2611.02396
AB - 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.
ER -