Magnetic dipole interaction ($U_{\mathrm{dd}}=\frac{{\mu }_0}{4\pi r^3}[{\mathbf{m}}_1\cdot {\mathbf{m}}_2-3({\mathbf{m}}_1\cdot \hat{\mathbf{r}})({\mathbf{m}}_2\cdot \hat{\mathbf{r}})]$)

The orientation-dependent interaction of two distant localized magnetic dipole moments. Its $r^{-3}$ scale makes close approach important in a concentrated magnetic-particle dispersion. Depending on geometry, it can favor chains, collective alignment or frustrated configurations.