A real-space renormalization group approach to the ferromagnetic Potts model on the two-dimensional octagonal quasi-periodic tiling

Abstract

A one-step real-space renormalization group (RSRG) transformation is used to study the ferromagnetic (FM) q-state Potts model on the two-dimensional (2D) octagonal quasi-periodic tiling (OQT). The critical exponents of the correlation length for different values of q and the critical temperature of the Ising model are obtained. The results are shown to be not sensitive to the choice of parameters. The comparison of the results with previous results for the OQT and the square lattice (SQL) seems to show that the universal classes of the q-state Potts models on the OQT and the SQL are the same for the range from q = 1 to q = 3, in accordance with previous research.