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 = ρ c 1 , and then again undergoes a re-entrant phase transition from the nematic phase to a disordered phase at ρ = ρ c 2 < 1.