# The isotropic-nematic transition for hard rods on a three--dimensional (3D) cubic lattice

## TL;DR

This study uses Monte Carlo simulations to analyze the isotropic-nematic transition of hard rods on a 3D lattice, revealing a weakly first-order transition with strong fluctuations and comparing results to theoretical predictions.

## Contribution

First detailed Monte Carlo analysis of the isotropic-nematic transition for hard rods on a 3D lattice, highlighting the transition's weakly first-order nature and discrepancies with theory.

## Key findings

- Transition occurs for rod length L >= 6.
- Weakly first-order transition with no clear density jump.
- Strong fluctuations observed near the transition.

## Abstract

Using grand canonical Monte Carlo (GCMC) simulations, we investigate the isotropic-nematic phase transition for hard rods of size Lx1x1 on a 3D cubic lattice. We observe such a transition for L >= 6. For L = 6, the nematic state has a negative order parameter, reflecting the co--occurrence of two dominating orientations. For L >= 7, the nematic state has a positive order parameter, corresponding to the dominance of one orientation. We investigate rod lengths up to L = 25 and find evidence for a very weakly first-order isotropic-nematic transition, while we cannot completely rule out a second order transition. It was not possible to detect a density jump at the transition, despite using large systems containing several 10^5 particles. The probability density distributions P(Q) from the GCMC simulations near the transition are very broad, pointing to strong fluctuations. Our results complement earlier results on the demixing (pseudonematic) transition for an equivalent system in 2D, which is presumably of Ising--type and is present for L >= 7. We compare our results to lattice fundamental measure theory (FMT) and find that FMT strongly overestimates nematic order and consequently predicts a strong first order transition. The rod packing fraction of the nematic coexisting states, however, agree reasonably well between FMT and GCMC.