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Numerical calculations of the average dipole-coupling energy $\barE_\mathrm{dip}$ in two-dimensional disordered magnetic nanostructures areperformed as function of the particle coverage $C$. We observe that $\barE_\mathrm{dip}$ scales as $\bar E_\mathrm{dip}\propto C^{\alpha^*}$ with anunusually small exponent $\alpha^*\simeq 0.8$--1.0 for coverages$C\lesssim20%$. This behavior is shown to be primarly given by thecontributions of particle pairs at short distances, which is intrinsicallyrelated to the presence of an appreciable degree of disorder. The value of$\alpha^*$ is found to be sensitive to the magnetic arrangement within thenanostructure and to the degree of disorder. For large coverages $C\gtrsim20%$we obtain $\bar E_\mathrm{dip}\propto C^\alpha$ with $\alpha=3/2$, in agreementwith the straighforward scaling of the dipole coupling as in a periodicparticle setup. Taking into account the effect of single-particle anisotropies,we show that the scaling exponent can be used as a criterion to distinguishbetween weakly interacting ($\alpha^* \simeq 1.0$) and strongly interacting($\alpha^* \simeq 0.8$) particle ensembles as function of coverage.Comment: accepted for publication in Phys.Rev.

Scaling behavior of the dipole-coupling energy in two-dimensional disordered magnetic nanostructures