  We study the ground-state properties of a system of dimers. Each dimer
consists in a pair of equivalent charges at a fixed distance, immersed in a
neutralizing homogeneous background. All charges interact pairwisely by Coulomb
potential. The dimer centers form a two-dimensional rectangular lattice with
the aspect ratio $\alpha\in [0,1]$ and each dimer is allowed to rotate around
its center. The previous numerical simulations, made for the more general
Yukawa interaction, indicate that only two basic dimer configurations can
appear: either all dimers are parallel or they have two different angle
orientations within alternating (checkerboard) sublattices. As the dimer size
increases, two second-order phase transitions, related to two kinds of the
symmetry breaking in dimer's orientations, were reported. In this paper, we use
a recent analytic method based on an expansion of the interaction energy in
Misra functions which converges quickly and provides an analytic derivation of
the critical behaviour. Our main result is that there exists a specific aspect
ratio of the rectangular lattice $\alpha^*=0.71410684000071\ldots$ which
divides the space of model's phases onto two distinct regions. If the lattice
aspect ratio $\alpha>\alpha^*$, we recover both types of the second-order phase
transitions and find that they are of mean-field type with the critical
exponent $\beta = 1/2$. If $\alpha<\alpha^*$, the phase transition associated
with the discontinuity of dimer's angles on alternating sublattices becomes of
first order. For $\alpha=\alpha^*$, the first- and second-order phase
transitions meet at the tricritical point, characterized by the different
critical index $\beta = 1/4$. Such phenomenon is known from literature about
the Landau theory of one-component fields, but in our two-component version the
scenario is more complicated.
