Abstract
We report results of a study of percolation on a two-dimensional Penrose quasilattice. After an extensive numerical analysis, we find that two-dimensional universality is obeyed. The scaling exponentsσ andτ have the values expected,τ=2.04 andσ=0.39, consistent with the universality class for percolation on a 2D periodic lattice. But the percolation thresholdp c=0.483, differs from other 2D lattices with the same average coordination number ¯z=4.
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We dedicate this paper to the memeory of Marc Kac. One of us (J.L.B.) had the good fortune to known him on many levels: as friend, fellow scientist, and co-worker for human rights. His insight, wisdom, and compassion will remain with us as a lasting legacy of his life.
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Lu, J.P., Birman, J.L. Percolation and scaling on a quasilattice. J Stat Phys 46, 1057–1066 (1987). https://doi.org/10.1007/BF01011156
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DOI: https://doi.org/10.1007/BF01011156