  We study the different phases of a system of monodispersed hard rods of
length $k$ on a cubic lattice using an efficient cluster algorithm which can
simulate densities close to the fully-packed limit. For $k\leq 4$, the system
is disordered at all densities. For $k=5,6$, we find a single density-driven
transition from a disordered phase to high density layered-disordered phase in
which the density of rods of one orientation is strongly suppressed, breaking
the system into weakly coupled layers. Within a layer, the system is
disordered. For $k \geq 7$, three density driven transitions are observed
numerically: isotropic to nematic to layered-nematic to layered-disordered. In
the layered-nematic phase, the system breaks up into layers, with nematic order
in each in each layer, but very weak correlation between the ordering direction
between different layers. We argue that the layered-nematic phase is a
finite-size effect, and in the thermodynamic limit, the nematic phase will have
higher entropy per site.
