Joyjit Kundu, R. Rajesh, Deepak Dhar, Jurgen F. Stilck
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 $k=7$. On the square lattice, 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 larger length scales. On the triangular lattice, the critical exponents are consistent with those of the two dimensional three-state Potts universality class. We study the correlations in the high-density non-nematic phase, and find evidence of a very large correlation length $\gtrsim 2000$.
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http://arxiv.org/abs/1211.2536
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