Abstract
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 \ensuremath{\nu} and \ensuremath{\gamma} are the same as in 2D periodic lattices whereas the different estimates of \ensuremath{\alpha} are not really consistent with the 2D periodic value. The infinite tiling critical temperature, ${\mathrm{kT}}_{c}/J\ensuremath{\approx}1.557,$ 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.
Published Version
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