



01331nas a2200157   4500008004100000245004000041210003900081260001400120300001100134490000800145520091900153100002301072700002101095700002001116856003701136       2023                        eng d00aSelf-dual quasiperiodic percolation0 aSelfdual quasiperiodic percolation  c2/27/2023  a0241370 v1073 a<p>How does the percolation transition behave in the absence of quenched randomness? To address this question, we study two nonrandom self-dual quasiperiodic models of square-lattice bond percolation. In both models, the critical point has emergent discrete scale invariance, but none of the additional emergent conformal symmetry of critical random percolation. From the discrete sequences of critical clusters, we find fractal dimensions of Df=1.911943(1) and Df=1.707234(40) for the two models, significantly different from Df=91/48=1.89583... of random percolation. The critical exponents ν, determined through a numerical study of cluster sizes and wrapping probabilities on a torus, are also well below the ν=4/3 of random percolation. While these new models do not appear to belong to a universality class, they demonstrate how the removal of randomness can fundamentally change the critical behavior.</p>1 aSommers, Grace, M.1 aGullans, Michael1 aHuse, David, A.  uhttps://arxiv.org/abs/2206.11290