A two species interacting system motivated by the density functional theory
for triblock copolymers contains long range interaction that affects
the two species differently. In a two species periodic assembly of
discs, the two species appear alternately on a lattice.
The minimal two species periodic assembly is the one with the least
energy per lattice cell area.
There is a parameter $b$ in $[0,1]$ and the type of the lattice associated
with the minimal assembly varies depending on $b$. There are several
threshold defined by a number $B=0.1867...$
If $b \in [0, B)$, the minimal assembly is associated with a rectangular
lattice whose ratio of the longer side and the
shorter side is in $[\sqrt{3}, 1)$;
if $b \in [B, 1-B]$, the minimal assembly is associated with a square lattice;
if $b \in (1-B, 1]$, the minimal assembly is associated with a
rhombic lattice with an acute angle in $[\frac{\pi}{3}, \frac{\pi}{2})$.
Only when $b=1$, this rhombic lattice is the hexagonal lattice.
None of the other values of $b$ yields the hexagonal lattice,
a sharp contrast to the situation for one species
interacting systems, where the hexagonal lattice is ubiquitously observed.