PreprintCC0arXiv
Disorder on the hyperbolic square lattice I: Anderson delocalization and absolutely continuous spectrum
Abstract
We study the Anderson model on hyperbolic lattices. The graph is the Cartesian product of the Euclidean lattice with the regular hyperbolic square lattice having five squares at each vertex. We prove the existence of absolutely continuous spectrum and the absence of singular spectrum on a deterministic set of positive measure at weak disorder, and for 0<λ≤2 when the single-site density is bounded below on [−1,1]. Truncated Cauchy distributions and controlled perturbations give purely absolutely continuous spectrum on intervals.
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BibTeX
@misc{becker2026disorder,
title = {{Disorder on the hyperbolic square lattice I: Anderson delocalization and absolutely continuous spectrum}},
author = {Simon Becker and Izak Oltman},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20798},
eprint = {2609.20798},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20798},
note = {CC0},
}
RIS
TY - UNPB
TI - Disorder on the hyperbolic square lattice I: Anderson delocalization and absolutely continuous spectrum
AU - Simon Becker
AU - Izak Oltman
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20798
UR - https://arxiv.org/abs/2609.20798
AB - We study the Anderson model on hyperbolic lattices. The graph is the Cartesian product of the Euclidean lattice with the regular hyperbolic square lattice having five squares at each vertex. We prove the existence of absolutely continuous spectrum and the absence of singular spectrum on a deterministic set of positive measure at weak disorder, and for 0<λ≤2 when the single-site density is bounded below on [−1,1]. Truncated Cauchy distributions and controlled perturbations give purely absolutely continuous spectrum on intervals.
ER -