Covariance-dependent participation scaling of Comtet disorder on open hyperbolic lattices
Abstract
Negative curvature makes the electrostatic Green function decay exponentially, producing a finite disorder-variance budget even as radial volume grows exponentially. We investigate whether this near-field concentration also determines wave-function participation on open hyperbolic lattices. A Gaussian control preserves the full one-site distribution of Comtet disorder at every vertex while removing its off-diagonal covariance. Complete-window participation ratios on {7,3} graphs with N=847,2240,5887 yield an effective-exponent difference of −0.028 at W/t=0.5 and +0.116 at W/t=3; both signs persist upon extending to N=15435. Size-resolved squared-kernel radii lie near 2.45ℓ on the larger graphs of this sequence, below the cutoff-matched continuum value 3.12ℓ. Distance-shell weights resolve the finite discrete measure associated with this shift, while higher participation moments and spacing ratios characterize the accompanying wave-function and spectral structure. A marginal-matched exponential-kernel family gives positive exponent contrasts at all five sampled kernel lengths at W/t=0.5,3, separating the Comtet response from a description based on the decay length alone. These results distinguish a concentrated variance budget from the covariance-dependent participation response of finite open hyperbolic systems.
Related
- Hyperbolic lattices with mass disorder: Phases and phase transitions
- Lieb-Schultz-Mattis constraints for hyperbolic lattices
- Finite-state automata for exact matrix product operators of tight-binding Hamiltonians: fractals, quasicrystals, trees and hyperbolic lattices
- The 2d Ising Model on Hyperbolic Lattices and the Role of Boundary Conditions
- Magnetic long-range order at finite temperature in two-dimensional hyperbolic lattices
BibTeX
@misc{li2026covariancedependent,
title = {{Covariance-dependent participation scaling of Comtet disorder on open hyperbolic lattices}},
author = {Wei Li and Yong Cheng},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01510},
eprint = {2611.01510},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01510},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Covariance-dependent participation scaling of Comtet disorder on open hyperbolic lattices
AU - Wei Li
AU - Yong Cheng
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01510
UR - https://arxiv.org/abs/2611.01510
AB - Negative curvature makes the electrostatic Green function decay exponentially, producing a finite disorder-variance budget even as radial volume grows exponentially. We investigate whether this near-field concentration also determines wave-function participation on open hyperbolic lattices. A Gaussian control preserves the full one-site distribution of Comtet disorder at every vertex while removing its off-diagonal covariance. Complete-window participation ratios on {7,3} graphs with N=847,2240,5887 yield an effective-exponent difference of −0.028 at W/t=0.5 and +0.116 at W/t=3; both signs persist upon extending to N=15435. Size-resolved squared-kernel radii lie near 2.45ℓ on the larger graphs of this sequence, below the cutoff-matched continuum value 3.12ℓ. Distance-shell weights resolve the finite discrete measure associated with this shift, while higher participation moments and spacing ratios characterize the accompanying wave-function and spectral structure. A marginal-matched exponential-kernel family gives positive exponent contrasts at all five sampled kernel lengths at W/t=0.5,3, separating the Comtet response from a description based on the decay length alone. These results distinguish a concentrated variance budget from the covariance-dependent participation response of finite open hyperbolic systems.
ER -