Monte Carlo Study of a Frustrated Ising Spin on a Quasi-Crystal

We use Monte Carlo techniques to study an Ising spin system on the HBS tiling, i.e., a two-dimensional decagonal quasicrystal. The nearest- (or second-nearest-) neighbor interaction is assumed ferromagnetic (or antiferromagnetic). We found three phases for this system, namely, paramagnetic, ferromagnetic, and spin-glass-like.