Physica A 269 (1999) 201–210 www.elsevier.com/locate/physa Site percolation on the Penrose rhomb lattice Robert M. Zi a ; ∗ , Filip Babalievski b a Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109-2136, USA b Institute of General and Inorganic Chemistry, Bulgarian Academy of Sciences, 1113 Soa, Bulgaria Received 10 April 1999 Abstract An epidemic analysis of cluster growth on the rhomb form of the Penrose lattice yields the site percolation threshold pc =0:58391 ± 0:00001. The corrections-to-scaling exponent  ≈ 0:7 is consistent with the value 0:77 ± 0:02 found here for the square lattice and triangular lattices. c  1999 Elsevier Science B.V. All rights reserved. 1. Introduction From the point of view of percolation, quasilattices (or aperiodic lattices) such as the Penrose lattice [1,2] (Fig. 1) have many interesting features. Like random lattices, they are non-uniform on a local scale, yet they also possess a long-range quasi-regularity. This quasi-regularity does not seem to change the university class from that of usual 2d percolation, as shown (to rather low precision, however) in early studies [3,4]. Recently, quasilattices have been used to test correlations between the critical thresholds p c and lattice properties. For this purpose they are particularly useful because of their range of local environments (coordination number and/or polygon arrangements) [5 –7]. In a recent work [7], Suding and Zi studied the relation of p c and a quantity that is essentially the lling factor f of Scher and Zallen [8] but generalized to allow for non-regular polygons in the lattice. A good correlation, for example, was found by tting p c (f) to a quadratic using the three known exact values: triangular (p c = 1= 2;f =  √ 3= 6), Kagom e(p c =1 − 2 sin = 18;f =  √ 3= 8), and the 3; 12 2 -lattice (p c = [1 − 2 sin = 18] 1=2 , f = [7 √ 3 − 12]), resulting in p c =0:94659 − 0:25100f − 0:26623f 2 : (1) * Corresponding author. Fax: +1-734 763-0459. E-mail addresses: rzi@umich.edu (R.M. Zi), fvb@ical.uni-stuttgart.de (F. Babalievski) 0378-4371/99/$ - see front matter c  1999 Elsevier Science B.V. All rights reserved. PII: S0378-4371(99)00166-1