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 $\approx k\ln [k/\ln k]$ for large $k$, and that the density of uncovered sites drops from a value $\approx (\ln k)/k^2$ 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 $d\ge 2$. We also present evidence of coexistence of nematic and disordered phases from Monte Carlo simulations for rods of length $9$ on the square lattice.

14 pages, 19 figures

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Cited by in corpus (4)

• Entropy of rigid k-mers on a square lattice
• Entropy of different phases formed by soft rods
• Phases of the hard-plate lattice gas on a three-dimensional cubic lattice
• Semi-flexible trimers on the square lattice in the full lattice limit