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We study the different phases of a system of monodispersed hard rods oflength $k$ on a cubic lattice using an efficient cluster algorithm which cansimulate densities close to the fully-packed limit. For $k\leq 4$, the systemis disordered at all densities. For $k=5,6$, we find a single density-driventransition from a disordered phase to high density layered-disordered phase inwhich the density of rods of one orientation is strongly suppressed, breakingthe system into weakly coupled layers. Within a layer, the system isdisordered. For $k \geq 7$, three density driven transitions are observednumerically: isotropic to nematic to layered-nematic to layered-disordered. Inthe layered-nematic phase, the system breaks up into layers, with nematic orderin each in each layer, but very weak correlation between the ordering directionbetween different layers. We argue that the layered-nematic phase is afinite-size effect, and in the thermodynamic limit, the nematic phase will havehigher entropy per site.

Different phases of a system of hard rods on three dimensional cubic lattice