The self-assembly scenario of the dipolar hard sphere (DHS) particles is not limited to linear chains: in our work we aim at describing the DHS fluid in terms of a network of chains and rings (the fundamental clusters) held together by branching points (defects).
We put forward a new method based on Monte Carlo grand-canonical simulations to precisely calculate partition functions at low densities and low temperature. Our approach is much faster than previously used canonical Monte Carlo simulations with large particle ensembles: this advantage in efficiency allows us reaching the part of the DHS phase diagram inaccessible before and observe the precursor of percolation. We present a detailed study of the structure of defects in dipolar hard sphere systems, introducing a systematic way of classifying inter-cluster connections according the their topology.
We confirm that for low concentrations and low temperatures, the majority of magnetic nanoparticles is aggregated in rings; for higher concentrations, low temperature clusters merge together into more complex branched structures. We find that, decreasing the value of the temperature, the relevant configuration is provided by four-way junctions arising from parallel or anti-parallel locally linear aggregate: a structure different from the one predicted by Tlusty and Safran as the responsible of a possible topological phase transition.
Our results allow us to describe the next hierarchical level of self-assembly in magnetic nano colloids: the aggregation of basic branched clusters into complex networks.
 S. S. Kantorovich, A.O. Ivanov, L. Rovigatti, J.M. Tavares and F. Sciortino, Phys. Chem. Chem. Phys. 17, 16601-16608 (2015)
 T. Tlusty and S. A. Safran, Science 290, 1328 (2000).