Long range antiferromagnetic order in Ising model simulations in a two-dimensional Penrose lattice

Long-range antiferromagnetic order was found in simulated annealing calculations for an Ising spin system on a two-dimensional Penrose lattice under Ruderman–Kittel–Kasuya–Yosida-like alternating exchange interactions at low temperatures. Two models of magnetic interactions resulted in the long-range antiferromagnetic order; a model of an antiferromagnetic interaction for the shortest distance and ferromagnetic interaction for the second and the third shortest distances, and a reversed sign model. Both models showed sharp magnetic diffraction spots with the same peak widths as the ordinary lattice diffraction, which indicates the long-range magnetic order extending over the whole system. The contrasts of the magnetic diffraction patterns were different from the patterns arising from the spin-independent scattering amplitudes from the Penrose lattice sites. The Patterson map analysis also confirmed the long-range nature of the antiferromagnetic order. The reversed-sign interaction model resulted in a stronger antiferromagnetic character than the non-reversed one.