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

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 (SARRs) model, the surface is represented by a two-dimensional 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 quasi-one-dimensional behavior in this regime. Finally, the universality class of the SARRs model, which has been subject of controversy, has been revisited.