Abstract
Anisotropic site dilution is introduced into the two-dimensional Penrose lattice by varying the seven-nearest-neighbor (7NN) site concentration ${p}_{7}$ from zero (no 7NN sites) to one (all 7NN sites present). A first-order phase transition line is found for the q=5 Potts model in the region ${p}_{7c}$${p}_{7}$\ensuremath{\le}1 which terminates at a critical point ${p}_{7c}$=0.941(3), conjectured to be in a new universality class.
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