  Monte Carlo (MC) simulations and finite-size scaling analysis have been
carried out to study the critical behavior in a submonolayer two-dimensional
gas of repulsive linear $k$-mers on a triangular lattice at coverage
$k/(2k+1)$. A low-temperature ordered phase, characterized by a repetition of
alternating files of adsorbed $k$-mers separated by $k+1$ adjacent empty sites,
is separated from the disordered state by a order-disorder phase transition
occurring at a finite critical temperature, $T_c$. The MC technique was
combined with the recently reported Free Energy Minimization Criterion Approach
(FEMCA), [F. Rom\'a et al., Phys. Rev. B, 68, 205407, (2003)], to predict the
dependence of the critical temperature of the order-disorder transformation.
The dependence on $k$ of the transition temperature, $T_c(k)$, observed in MC
is in qualitative agreement with FEMCA. In addition, an accurate determination
of the critical exponents has been obtained for adsorbate sizes ranging between
$k=1$ and $k=3$. For $k>1$, the results reveal that the system does not belong
to the universality class of the two-dimensional Potts model with $q=3$ ($k=1$,
monomers). Based on symmetry concepts, we suggested that the behavior observed
for $k=1, 2$ and 3 could be generalized to include larger particle sizes ($k
\geq 2$).
