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.

1 aSommers, Grace, M.1 aGullans, Michael, J.1 aHuse, David, A. uhttps://arxiv.org/abs/2206.11290