Non-frustrated Ferromagnetic Ising Model on the Quasiperiodic Octagonal Tiling: Finite-Size Behaviour

Abstract

The non-frustrated ferromagnetic Ising model on the quasiperiodic octagonal tiling is studied by means of Monte-Carlo simulations. From a finite-size scaling analysis of octagonal tilings with free boundary conditions, the critical temperature is estimated at kTc/J = 2.39 ± 0.01 and the critical exponents v, β and γ are in reasonable agreement with previous studies on the Penrose tiling. This strongly suggests that the two-dimensional ferromagnetic Ising model on quasiperiodic tilings and on periodic lattices belong to the same universality class.