Magnetic ordering of systems of nanodisks with quenched positional disorder

The effect of positional disorder in systems of single domain ferromagnetic nanodisks placed on a two-dimensional square lattice is studied by Monte Carlo simulations. Nanodisks are treated as magnetic dipoles pointing along one of the two principal axes of the lattice. Disorder is introduced displacing each nanodisk by (δx, δy) from its regular lattice position, where δx is randomly chosen within the interval 0 ≤ δx ≤ Δ and analogously for δy. Two different regimes are found: for Δ < Δ0 = 0.18(2) (in units of lattice spacing) a thermally driven transition between a paramagnetic and a dipolar antiferromagnetic phase with a critical exponent α/ν changing continuously with Δ; for Δ ≥ Δ0 a paramagnetic phase covering the whole T > 0 range. Plots of the spin-glass overlap parameter versus temperature T or lattice size L seem to exclude an equilibrium spin-glass phase in the latter regime.