  The critical behavior of adsorbed monomers that reversibly polymerize into
linear chains with restricted orientations relative to the substrate has been
studied. In the model considered here, which is known as self-assembled rigid
rods (SAARs) model, the surface is represented by a twodimensional lattice and
a continuous orientational transition occurs as a function of temperature and
coverage. The phase diagrams were obtained for the square, triangular and
honeycomb lattices by means of Monte Carlo simulations and finite-size scaling
analysis. The numerical results were compared with Bethe-Peierls analytical
predictions about the orientational transition for the square and triangular
lattices. The analysis of the phase diagrams, along with the behavior of the
critical average rod lengths, showed that the critical properties of the model
do not depend on the structure of the lattice at low temperatures (coverage),
revealing a one-dimensional behavior in this regime. Finally, the universality
class of the SAARs model, which has been subject of controversy, has been
revisited.
