High Dimensional Approach to Antiferromagnetic Aperiodic Spin Systems

Abstract

Monte Carlo approaches to aperiodic spin systems have found a range of antiferromagnetic ground states for both classical and quantum spins. In each case, the spin calculations have been undertaken on quasilattices in the appropriate dimension i.e. 1D for a Fibonacci chain, 2D for a Penrose tiling etc. Here we show that high dimension spin models can be calculated using the simplest of spin Hamiltonians, and that the projection of these high dimensional spins reproduces antiferromagnetic ground states in the ‘correct’ dimension. We also show a model for an atomistic antiferromagnetic quasicrystal, as derived using this method.