Critical behavior of SIS model on two-dimensional quasiperiodic tilings

We investigated the critical behavior of SIS (susceptible-infected-susceptible) model on Penrose and Ammann-Beenker quasiperiodic tilings by means of numerical simulations and finite size scaling technique. We used the reactivation dynamics, which consists of inserting a spontaneous infected particle without contact in the system when infection dies out, to avoid the dynamics being trapped in the absorbing state. We obtained the mean infection density, its fluctuation and 5-order Binder ratio, in order to determine the universality class of the system. We showed that the system still obeys two-dimensional directed percolation universality class, in according to Harris-Barghathi-Vojta criterion, which states quasiperiodic order is irrelevant for this system and do not induce any change in the universality class. Our results are in agreement with a previous investigation of the contact process model on two-dimensional Delaunay triangulations, which still obeys directed percolation universality class according to the same criterion.