Static critical behavior of a weakly frustrated Ising model on the octagonal tiling.

Abstract

The static critical behavior of a weakly frustrated ferromagnetic Ising model on the two-dimensional (2D) quasiperiodic octagonal tiling is studied by means of Monte Carlo simulations and finite-size scaling analysis. Our results strongly suggest that this frustrated Ising model on the octagonal tiling belongs to the same universality class as the ferromagnetic Ising model on 2D periodic lattices. The infinite tiling critical temperature, ${\mathit{kT}}_{\mathit{c}}$/J=1.49\ifmmode\pm\else\textpm\fi{}0.02, agrees with previous studies indicating that tendency to ferromagnetic ordering is higher in quasiperiodic tilings than in periodic lattices. \textcopyright{} 1996 The American Physical Society.