# Different phases of a system of hard rods on three dimensional cubic lattice

## TL;DR

This study investigates the phase behavior of hard rods on a cubic lattice, revealing multiple density-driven phase transitions and the emergence of layered phases, with implications for understanding ordering in constrained systems.

## Contribution

The paper introduces an efficient cluster algorithm to simulate high-density phases of hard rods and characterizes complex phase transitions, including layered and nematic phases, on a cubic lattice.

## Key findings

- For k ≤ 4, the system remains disordered at all densities.
- For k=5,6, a single transition to layered-disordered phase occurs.
- For k ≥ 7, multiple transitions including isotropic to nematic phases are observed.

## Abstract

We study the different phases of a system of monodispersed hard rods of length $k$ on a cubic lattice using an efficient cluster algorithm which can simulate densities close to the fully-packed limit. For $k\leq 4$, the system is disordered at all densities. For $k=5,6$, we find a single density-driven transition from a disordered phase to high density layered-disordered phase in which the density of rods of one orientation is strongly suppressed, breaking the system into weakly coupled layers. Within a layer, the system is disordered. For $k \geq 7$, three density driven transitions are observed numerically: isotropic to nematic to layered-nematic to layered-disordered. In the layered-nematic phase, the system breaks up into layers, with nematic order in each in each layer, but very weak correlation between the ordering direction between different layers. We argue that the layered-nematic phase is a finite-size effect, and in the thermodynamic limit, the nematic phase will have higher entropy per site.