Critical behavior of long linear k-mers on honeycomb lattices

Monte Carlo (MC) simulations, finite-size scaling and theoretical analysis have been carried out to study the critical behavior of long linear particles of length k (k-mers) on honeycomb lattices. A nematic phase, characterized by a big domain of parallel k-mers, is separated from the isotropic state, by a continuous transition occurring at a finite density θc. Our study allowed: (1) to determine the minimum value of k (kmin), which allows the formation of the nematic phase, being kmin=11; (2) to predict the dependence of θc on k, being θc(k)∝k−1; and (3) to obtain the critical exponents, which indicate that the transition belongs to the 2D three-state Potts universality class.