Sommers, G.
, Gullans, M.
and Huse, D.
(2023),
Self-dual quasiperiodic percolation, Physical Review E, [online], https://doi.org/10.1103/PhysRevE.107.024137, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=935725
(Accessed October 3, 2025)
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Self-dual quasiperiodic percolation
Published
Author(s)
Grace Sommers, , David Huse
Abstract
How does the percolation transition behave in the absence of quenched randomness? To address this question, we study a nonrandom self-dual quasiperiodic model of square-lattice bond percolation. Through a numerical study of cluster sizes and wrapping probabilities on a torus, we find critical exponent ν=0.87±0.05 and cluster fractal dimension Df =1.91194±0.00008, significantly different from the ν = 4/3, Df = 91/48 = 1.89583... of random percolation. The critical point has an emergent discrete scale invariance, but none of the additional emergent conformal symmetry of critical random percolation.Citation
Physical Review E
Volume
107
Issue
2
Pub Type
Journals
Download Paper
Keywords
Percolation, quasiperiodicity, critical phenomena
Citation
Issues
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Created February 27, 2023, Updated March 14, 2023