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Self-dual quasiperiodic percolation

Published

Author(s)

Grace Sommers, Michael Gullans, 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

Keywords

Percolation, quasiperiodicity, critical phenomena

Citation

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 February 29, 2024)
Created February 27, 2023, Updated March 14, 2023