We present the first real-space analysis on a single-particle level of the dipolar chains and branched clusters self-assembling in magnetic fluids in zero field. Spatial correlations and chain-length distributions directly obtained from tracked particle positions in vitrified films of synthetic magnetic (${\mathrm{Fe}}_3{\mathrm{O}}_4$) dispersions provide a quantitative test for simulations and theory of dipolar fluids. A pertinent example is the cluster-size distribution that can be analyzed with a one-dimensional aggregation model to yield a dipolar attraction energy that agrees well with the dipole moment found from independent magnetization measurements.

• Received 12 August 2005

DOI:https://doi.org/10.1103/PhysRevLett.96.037203