# The isotropic-to-nematic transition in a two-dimensional fluid of hard needles : a finite-size scaling study

## TL;DR

This study uses simulations and finite size scaling to analyze the isotropic-to-nematic phase transition in a 2D hard needle fluid, confirming it as a Kosterlitz-Thouless transition with specific critical exponents.

## Contribution

It provides the first direct measurement of critical exponents confirming the Kosterlitz-Thouless nature of the transition in this system.

## Key findings

- Transition is of the Kosterlitz-Thouless type with eta=1/4 and beta=1/8.
- Chemical potential shift matches theoretical predictions.
- Density fluctuations show singular behavior without divergence.

## Abstract

The isotropic-to-nematic transition in a two-dimensional fluid of hard needles is studied using grand canonical Monte Carlo simulations, multiple histogram reweighting, and finite size scaling. The transition is shown to be of the Kosterlitz-Thouless type, via a direct measurement of the critical exponents eta and beta, of the susceptibility and order parameter, respectively. At the transition, eta=1/4 and beta=1/8 are observed, in excellent agreement with Kosterlitz-Thouless theory. Also the shift in the chemical potential of the nematic susceptibility maximum with system size is in good agreement with theoretical expectations. Some evidence of singular behavior in the density fluctuations is observed, but no divergence, consistent with a negative specific heat critical exponent. At the transition, a scaling analysis assuming a conventional critical point also gives reasonable results. However, the apparent critical exponent beta_eff obtained in this case is not consistent with theoretical predictions.