RKKY Interactions and Low-Temperature Behaviour of Spins in Quasiperiodic Tilings

We study the structure of the Ruderman-Kittel-Kasuya-Yosida interactions for selected quasiperiodic tilings. The interaction energies between the magnetic impurities in these systems are computed by a continued fraction expansion for the Green function of the conduction electrons. Based on these results we study the alignment of the magnetic moments in the Ammann-Beenker tiling by Monte Carlo simulations. In particular, we are interested in the structure of the magnetic ground state and the low-temperature behaviour for the Ising model.