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The critical behavior of adsorbed monomers that reversibly polymerize intolinear chains with restricted orientations relative to the substrate has beenstudied. In the model considered here, which is known as self-assembled rigidrods (SAARs) model, the surface is represented by a twodimensional lattice anda continuous orientational transition occurs as a function of temperature andcoverage. The phase diagrams were obtained for the square, triangular andhoneycomb lattices by means of Monte Carlo simulations and finite-size scalinganalysis. The numerical results were compared with Bethe-Peierls analyticalpredictions about the orientational transition for the square and triangularlattices. The analysis of the phase diagrams, along with the behavior of thecritical average rod lengths, showed that the critical properties of the modeldo not depend on the structure of the lattice at low temperatures (coverage),revealing a one-dimensional behavior in this regime. Finally, the universalityclass of the SAARs model, which has been subject of controversy, has beenrevisited.

Critical behavior of self-assembled rigid rods on two-dimensional lattices: Bethe-Peierls approximation and Monte Carlo simulations