Abstract:
Systems of particles with hard core interactions are used to study phase transitions in equilibrium statistical mechanics. Lattice models are analytically more tractable. The problem of hard rods of length k on lattices is well studied. The system undergoes two transitions. First from a disordered phase to an orientationally aligned nematic phase, then from the nematic phase to a disordered phase again, as the density is increased. The first transition is well studied. However, the second transition remains a mystery - there are inconclusive results, or sometimes even contradictory results. We focused on numerically studying the problem of phase transitions in hard rigid rods of length k on a two dimensional square lattice. First using simple arguments we predicted the behaviour of quantities like the chemical potential, the density and the entropy near the transition as a function of k for a d−dimensional hypercubic lattice. We tested these predictions by studying the k×∞ lattice. We introduced a toy model for the second transition of hard rods on a 2-d square lattice, and argued that the asymptotic behaviour of the chemical potential, and density of holes is the same as that found for the k × ∞ lattice for large k. We gave evidence that the transition from the nematic phase to the high-density disordered phase is a first order transition.
