Nematic-disordered phase transition in systems of long rigid rods on two-dimensional lattices

We study the phase transition from a nematic phase to a high-density disordered phase in systems of long rigid rods of length k on the square and triangular lattices. We use an efficient Monte Carlo scheme that partly overcomes the problem of very large relaxation times of nearly jammed configurations. The existence of a continuous transition is observed on both lattices for $k=7$. We study correlations in the high-density disordered phase, and we find evidence of a crossover length scale ξ*1400 on the square lattice. For distances smaller than ξ*, correlations appear to decay algebraically. Our best estimates of the critical exponents differ from those of the Ising model, but we can not rule out a crossover to Ising universality class at length scales ξ*. On the triangular lattice, the critical exponents are consistent with those of the two-dimensional three-state Potts universality class.