Isotropic-Nematic-Disorder Transitions in a System of Long Rods on a Lattice

We consider a system of long rods with only excluded volume interaction on two dimensional lattices. As the density of rods is increased from zero, the system undergoes a transition from a disordered isotropic phase to an ordered nematic phase. We demonstrate the existence of a second transition from the nematic phase to a disordered phase at high densities. The critical exponents are determined numerically, and shown to be different from the Ising universality class. We also present an analytic solution to the problem within the Bethe approximation. In addition, results for hard objects of different shapes will also be discussed.