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Critical behavior of repulsive lineark-mers on square lattices at half coverage: Theory and Monte Carlo simulations

Monte Carlo (MC) simulations have been used to study the critical behavior of repulsive linear k-mers on square lattices at 50% coverage. A (2k×2) ordered phase, characterized by a repetition of alternating files of adsorbed k-mers separated by k adjacent empty sites, was found. This ordered phase is separated from the disordered state by a order-disorder phase transition occurring at a critical temperature T c , which presents an intriguing dependence with the size k of the adsorbed molecules. In addition, two analytical techniques were combined with Monte Carlo simulations to predict the critical temperature of the order-disorder transformation. The first is based on a detailed mean-field approximation (DMFA), considering the exact interactions between the k-mers belonging to a region y (the cluster) and a mean-field interaction with the rest outside y. Different sizes for y (k×1,k×2,2k×1,2k×2) were used in the calculations in order to discuss its influence in the determination of T c . The second approach is based on a free energy minimization criterion (FEMCA). The dependence on k of the transition temperature T c (k) observed in MC is in remarkable qualitative agreement with DMFA and FEMCA. Both allow us to interpret the physical meaning of the mechanisms underlying the observed transitions.