When does a topological-sector escape count? Definition-sensitive finite-size first-passage statistics across planar XY models

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Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-18
DOI
https://doi.org/10.5281/zenodo.22833021
Primary Topic
Nonlinear Dynamics and Pattern Formation
Type
preprint
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preprint

When does a topological-sector escape count? Definition-sensitive finite-size first-passage statistics across planar XY models

Egemen Ekinci
Zenodo (CERN European Organization for Nuclear Research)
Nonlinear Dynamics and Pattern Formation
preprint

When does a topological-sector escape count? Definition-sensitive finite-size first-passage statistics across planar XY models

Egemen Ekinci
preprint en

Abstract

Preprint of the manuscript "When does a topological-sector escape count? Definition-sensitive finite-size first-passage statistics across planar XY models", deposited together with the complete data and code package for the study. Topological-sector freezing is a dynamical signature of the low-temperature phase of Berezinskii-Kosterlitz-Thouless (BKT) systems, but short recrossings make the first-passage event definition nonunique. We test the sensitivity of topological escape across the two-dimensional XY model, the harmonic XY (HXY) model, and an elementary lattice-field electrolyte. We combine 288 public L=64 trajectories with 864 newly generated L=8, L=16, and L=32 trajectories, giving 48 independent local-Metropolis runs per model, size, and reduced-temperature condition. No five-frame persistent escape occurred in any low-temperature run over 10,000 observations. At high temperature, the XY four-size log-log RMST slope changed from -0.247 (95% bootstrap CI -0.443 to -0.054) for a one-frame event to +0.106 (-0.013 to +0.226) for a five-frame event. A separate 288-trajectory L=64 reproduction batch agreed with the public primary one-frame statistics. A prespecified 96-trajectory electrolyte extension reduced the five-frame public-versus-fresh RMST ratio from 1.723 (1.124 to 2.719) to 1.448 (0.995 to 2.207), with Holm-adjusted log-rank p=0.177. Supplemental L=8, L=16, and L=32 energy validation gave a maximum split-Rhat of 1.015. Topological first passage therefore distinguishes stable and mobile regimes, but its finite-size slope is not invariant to how an escape is confirmed. Event persistence and recrossing diagnostics must be specified before escape-time scaling is used as evidence for RG universality. The central conclusion is methodological rather than a claim about the BKT transition itself. Contents: the manuscript (PDF and DOCX), and BKT_Reproducibility_Package.tar.gz, which contains the generated trajectories, the deterministic configurations and seeds, the L=8/L=16/L=32 energy-validation traces, the independent matched L=64 reproduction batch, the disjoint-seed 96-trajectory L=64 electrolyte follow-up, the analysis code, the machine-readable results, and the manuscript figures. A standalone SHA-256 checksum and a concise reproduction guide (README.md) are supplied alongside the archive. Version 2.0.0 adds the manuscript to the version 1.0.0 data and code package. Preprint. Not peer reviewed. This work was produced with substantial AI assistance (Claude, Anthropic). The author takes full responsibility for the content.

Zenodo (CERN European Organization for Nuclear Research)
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Nonlinear Dynamics and Pattern Formation
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