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.
, Gullans, M.
and Huse, D.
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 June 7, 2023)