Long-range magnetic order in models for rare-earth quasicrystals

Understanding the impact of the unique electronic structure of rare-earth quasicrystals on their magnetic properties has been a long-standing problem in the study of these fascinating materials. The issue is addressed here by studying the RKKY interaction of Ising spins that is mediated by electrons on a tight-binding quasiperiodic tiling. After deriving the form of the RKKY interaction, the authors examine the statistical properties of the resulting model using extensive Monte Carlo simulations. They show that, despite the lack of periodicity and the frustrated nature of the interaction between spins, the system displays long-range magnetic quasiperiodic order at low temperatures.