Critical temperature of the non-frustrated ferromagnetic ising model on the quasiperiodic octagonal tiling

Abstract

The critical temperature of some non-frustrated ferromagnetic Ising spin systems on the two-dimensional octagonal tiling is calculated by Monte Carlo simulations using the simulated annealing method. The ferromagnetic interactions are limited to the third neighbours ( J 1, J 2, J 3) where only J 2 is a percolating interaction. The infinite-tiling critical temperature is estimated at kT c/ J = 2.39 ± 0.02 ( J 2 = J and J 1 = J 3 = 0), kT c/ J = 3.05 ± 0.03 ( J 2 = J 1 = J and J 3 = 0), kT c/ J = 3.60 ± 0.04 ( J 2 = J 3 = J and J 1 = 0) and kT c/〈 z〉 J is generally slightly higher in the octagonal tiling than in the square and triangular lattices indicating that the tendency to ferromagnetic ordering is higher in quasiperiodic tilings. It is found that the critical temperature, T c, varies linearly with the different exchange integrals.