  The self-assembly in two dimensions of spherical magnets in strong magnetic
field is addressed theoretically. %% It is shown that the attraction and
assembly of parallel magnetic chains is the result of a delicate interplay of
dipole-dipole interactions and short ranged excluded volume correlations. %%
Minimal energy structures are obtained by numerical optimization procedure as
well as analytical considerations. For a small number of constitutive magnets
$N_{\rm tot}\leq26$, a straight chain is found to be stable. In the regime of
larger $N_{\rm tot}\geq27$, the magnets form \textit{two touching} chains with
equally long tails at both ends. We succeed to identify the transition from
\textit{two} to \textit{three} touching chains at $N_{\rm tot}=129$.
