Recursive percolation.
We introduce a simple lattice model in which percolation is constructed on top of critical percolation clusters, and find compelling numerical evidence that it can be repeated recursively any number n of generations. In two dimensions, we determine the percolation thresholds up to n=5. The corresponding critical clusters become more and more compact as n increases, and define universal scaling functions of the standard two-dimensional form and critical exponents that are distinct for any n. This family of exponents differs from previously known universality classes, and cannot be accommodated by existing analytical methods. We confirm that recursive percolation is well defined also in three dimensions.
Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
Xuan-Wen
XW
Liu
Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
Youjin
Y
Deng
Laboratoire de Physique Théorique, École Normale Supérieure, 24 rue Lhomond, 75231 Paris, France.|Université Pierre et Marie Curie, 4 place Jussieu, 75252 Paris, France.
Jesper Lykke
JL
Jacobsen
D003198:Computer Simulation; D017709:Fractals; D008962:Models, Theoretical; D009010:Monte Carlo Method; D016062:Porosity; D011336:Probability