The phase transition from nematic to high-density disordered phase in a system of hard rods on a lattice

Abstract

A system of hard rigid rods of length k on hypercubic lattices is known to undergo two phases transitions when chemical potential is increased: from a low density isotropic phase to an intermediate density nematic phase, and on further increase to a high-density phase with no orientational order. In this paper, we argue that, for large k, the second phase transition is a first order transition with a discontinuity in density in all dimensions greater than 1. We show the chemical potential at the transition is ≈ k ln[k/ ln k] for large k, and that the density of uncovered sites drops from a value ≈ (ln k)/k 2 to a value of order exp(−ak), where a is some constant, across the transition. We conjecture that these results are asymptotically exact, in all dimensions d ≥ 2. We also present evidence of coexistence of nematic and disordered phases from Monte Carlo simulations for rods of length 9 on the square lattice.

Entropy of fully-packed rigid rods on generalized Husimi trees: a route to the square lattice limit

“…Even using a new Monte Carlo scheme which reduces the long relaxation times in the high density region and was introduced in Ref. [14], which leads to more precise results for the second transition, its universality class is still not clear, and actually recent results show that it is actually discontinuous for large k [15].…”