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

Abstract

We study the structure of the RudermanKittelKasuyaYosida 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 AmmannBeenker 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.