The 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 $ξ^* \gtrsim 1400$, 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 cannot rule out a crossover to Ising universality class at length scales $\gg ξ^*$. On the triangular lattice, the critical exponents are consistent with those of the two dimensional three-state Potts universality class.

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