At high densities fluids of strongly dipolar spherical particles exhibit
spontaneous long-ranged orientational order. Typically, due to demagnetization
effects induced by the long range of the dipolar interactions, the
magnetization structure is spatially inhomogeneous and depends on the shape of
the sample. We determine this structure for a cubic sample by the free
minimization of an appropriate microscopic density functional using simulated
annealing. We find a vortex structure resembling four domains separated by four
domain walls whose thickness increases proportional to the system size L. There
are indications that for large L the whole configuration scales with the system
size. Near the axis of the mainly planar vortex structure the direction of the
magnetization escapes into the third dimension or, at higher temperatures, the
absolute value of the magnetization is strongly reduced. Thus the orientational
order is characterized by two point defects at the top and the bottom of the
sample, respectively. The equilibrium structure in an external field and the
transition to a homogeneous magnetization for strong fields are analyzed, too.Comment: 17 postscript figures included, submitted to Phys. Rev.
