We study magnetism in simple models for rare earth quasicrystals by means of
a two-step theoretical approach. First, we compute RKKY interactions from a
tight-binding Hamiltonian defined on a two-dimensional quasiperiodic tiling.
Second, we examine the statistical mechanics of Ising spins coupled via these
interactions using Monte Carlo simulations. We find the emergence of strongly
coupled spin clusters with significantly weaker inter-cluster coupling, and a
transition to a low-temperature phase that has long-range order evidenced by a
finite domain wall tension.Comment: restructuring of paper and update of numerical results, 5 pages, 4
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