Two-dimensional array of magnetic particles: The role of an interaction cutoff

Based on theoretical results and simulations, in two-dimensional arrangements of a dense dipolar particle system, there are two relevant local dipole arrangements: (1) a ferromagnetic state with dipoles organized in a triangular lattice and (2) an antiferromagnetic state with dipoles organized in a square lattice. In order to accelerate simulation algorithms, we search for the possibility of cutting off the interaction potential. Simulations on a dipolar two-line system lead to the observation that the ferromagnetic state is much more sensitive to the interaction cutoff R than the corresponding antiferromagnetic state. For $R\gtrsim 8$ (measured in particle diameters) there is no substantial change in the energetical balance of the ferromagnetic and antiferromagnetic state and the ferromagnetic state slightly dominates over the antiferromagnetic state, while the situation is changed rapidly for lower interaction cutoff values, leading to the disappearance of the ferromagnetic ground state. We studied the effect of bending ferromagnetic and antiferromagnetic two-line systems and observed that the cutoff has a major impact on the energetical balance of the ferromagnetic and the antiferromagnetic state for $R\lesssim 4.$ Based on our results we argue that $R\approx 5$ is a reasonable choice for dipole-dipole interaction cutoff in two-dimensional dipolar hard sphere systems, if one is interested in local ordering.