  We numerically study a mesoscopic system consisting of magnetic nanorings in
the presence of thermal magnetization fluctuations. We find the formation of
dipolar-field-mediated ``bonds" promoting the formation of annuli clusters,
where the amount of bonds between two rings varies between zero and two. This
system resembles the formation of polymers from artificial atoms, which in our
case are the annuli and where the valency of the atom is set by the ring
multipolarity. We investigate the thermodynamic properties of the resulting
structures, and find a transition associated with the formation of the bonds.
In addition, we find that the system has a tendency to form topological
structures, with a distinct critical temperature in relation to the one for
bond formation.
