Spin quantum Hall transition on random networks: exact critical exponents via quantum gravity
Mesoscale and Nanoscale Physics
2026-02-02 v1 Disordered Systems and Neural Networks
Mathematical Physics
math.MP
Abstract
We solve the problem of the spin quantum Hall transition on random networks using a mapping to classical percolation that focuses on the boundary of percolating clusters. Using tools of two-dimensional quantum gravity, we compute critical exponents that characterize this transition and confirm that these are related to the exponents for the regular (square) network through the KPZ relation. Our results demonstrate the relevance of the geometric randomness of the networks and support conclusions of numerical simulations of random networks for the integer quantum Hall transition.
Cite
@article{arxiv.2601.22639,
title = {Spin quantum Hall transition on random networks: exact critical exponents via quantum gravity},
author = {Esteban Macías and Ilya Gruzberg and Eldad Bettelheim},
journal= {arXiv preprint arXiv:2601.22639},
year = {2026}
}