Critical behavior of long straight rigid rods on two-dimensional lattices: Theory and Monte Carlo simulations


The critical behavior of long straight rigid rods of length kk (kk-mers) on square and triangular lattices at intermediate density has been studied. A nematic phase, characterized by a big domain of parallel kk-mers, was found. This ordered phase is separated from the isotropic state by a continuous transition occurring at a intermediate density θc\theta_c. Two analytical techniques were combined with Monte Carlo simulations to predict the dependence of θc\theta_c on kk, being θc(k)k1\theta_c(k) \propto k^{-1}. The first involves simple geometrical arguments, while the second is based on entropy considerations. Our analysis allowed us also to determine the minimum value of kk (kmin=7k_{min}=7), which allows the formation of a nematic phase on a triangular lattice.Comment: 23 pages, 5 figures, to appear in The Journal of Chemical Physic

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