On the orientational ordering of long rods on a lattice

We argue that a system of straight rigid rods of length k on a square lattice with only hard-core interactions shows two phase transitions as a function of density ρ for k ≥ 7. The system undergoes a phase transition from the low-density disordered phase to a nematic phase as ρ is increased from 0 at ρ = ρc1, and then again undergoes a re-entrant phase transition from the nematic phase to a disordered phase at ρ = ρc2 < 1