Static critical behavior of the ferromagnetic Ising model on the quasiperiodic octagonal tiling

Abstract

The static critical behavior of the nonfrustrated ferromagnetic Ising model on the two-dimensional (2D) quasiperiodic octagonal tiling with free boundary conditions is studied by means of Monte Carlo simulations and finite-size scaling analysis. Several estimates of the critical temperature are clearly consistent and provide the final value ${\mathit{kT}}_{\mathit{c}}$/J=2.39\ifmmode\pm\else\textpm\fi{}0.01. This result shows that tendency to ferromagnetic ordering is higher in the octagonal quasilattice than in the square lattice (the mean number of interacting neighbors is equal to 4 in the two lattices). The estimates of the static critical exponents \ensuremath{\nu}, \ensuremath{\beta}, and \ensuremath{\gamma} are in agreement with previous studies on the Penrose tiling and evidence that the nonfrustrated ferromagnetic Ising model on 2D quasilattices belongs to the same universality class as the ferromagnetic Ising model on 2D periodic lattices.