Self-dual quasiperiodic percolation

Grace M. Sommers, Michael J. Gullans, David A. Huse

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish (US)
Article number024137
JournalPhysical Review E
Issue number2
StatePublished - Feb 2023

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability


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