Finite-size behavior of the three-state Potts model on the quasiperiodic octagonal tiling

The static critical behavior of the three-state Potts model on the two-dimensional (2D) quasiperiodic octagonal tiling with free boundary conditions is investigated by means of the importance-sampling Monte Carlo, method and the single histogram technique. The results strongly suggest that the static, critical exponents nu and gamma are the same as in 2D periodic lattices whereas the different estimates of alpha are not really consistent with the 2D periodic value. The infinite tiling critical temperature, kT(c)/J approximate to 1.557, is slightly higher than the critical temperature of the three-state Potts model on the square lattice, in agreement with previous studies on the Ising model on quasiperiodic tilings. [S0163-1829(97)04441-X].