  We study the phase transition in a system composed of dimers interacting with
each other via a nearest-neighbor (NN) exchange $J$ and competing interactions
taken from a truncated dipolar coupling. Each dimer occupies a link between two
nearest sites of a simple cubic lattice. We suppose that dimers are
self-avoiding and can have only three orientations which coincide with the $x$,
$y$ or $z$ direction. The interaction $J$ is attractive if the two dimers are
parallel with each other at the NN distance, zero otherwise. The truncated
dipolar interaction is characterized by two parameters: its amplitude $D$ and
the cutoff distance $r_c$. Using the steepest-descent method, we determine the
ground-state (GS) configuration as functions of $D$ and $r_c$. We then use
Monte Carlo simulations to investigate the nature of the low-temperature phase
and to determine characteristics of the phase transition from the ordered phase
to the disordered phase at high temperatures at a given dimer concentration. We
show that as the temperature increases, dimers remain in the compact state and
the transition from the low-$T$ compact phase to the disordered phase where
dimers occupy the whole space is of second order when $D$ is small, but it
becomes of first order for large enough $D$, for both polarized and non
polarized dimers. This transition has a resemblance with the unfolding polymer
transition. The effect of $r_c$ is discussed.
