# Nematic and gas-liquid transitions for sticky rods on square and cubic lattices

## TL;DR

This study uses grand-canonical Monte Carlo simulations to explore how sticky rod particles behave on square and cubic lattices, revealing complex phase transitions including gas-liquid and nematic ordering.

## Contribution

It provides new insights into the phase diagram of sticky rods on lattices, highlighting differences from continuum nematic transitions and the effects of attractions.

## Key findings

- On square lattices, attractions stabilize the isotropic phase initially.
- On cubic lattices, the nematic transition remains weak first order despite attractions.
- Near gas-liquid transition, the nematic coexistence gap widens significantly.

## Abstract

Using grand-canonical Monte Carlo simulations, we investigate the phase diagram of hard rods of length $L$ with additional contact (sticky) attractions on square and cubic lattices. The phase diagram shows a competition between gas-liquid and ordering transitions (which are of demixing type on the square lattice for $L \ge 7$ and of nematic type on the cubic lattice for $L \ge 5$). On the square lattice, increasing attractions initially lead to a stabilization of the isotropic phase. On the cubic lattice, the nematic transition remains of weak first order upon increasing the attractions. In the vicinity of the gas-liquid transition, the coexistence gap of the nematic transition quickly widens. These features are different from nematic transitions in the continuum.