Restricted orientation "liquid crystal" in two dimensions: Isotropic-nematic transition or liquid-gas (?)

TL;DR

This paper uses Monte Carlo simulations to study a two-dimensional Zwanzig fluid, revealing a liquid-gas phase transition with Ising criticality and discussing the effects of multiple particle orientations on symmetry and phase behavior.

Contribution

It identifies the phase transition as liquid-gas type rather than isotropic-nematic, contrasting previous interpretations, and explores symmetry emergence with increased particle orientations.

Findings

Observed a phase transition with Ising critical behavior.

Identified the transition as liquid-gas type, not isotropic-nematic.

Extended analysis to multiple orientations, linking to q-state Potts models.

Abstract

We present Monte Carlo simulation results of the two-dimensional Zwanzig fluid, which consists of hard line segments which may orient either horizontally or vertically. At a certain critical fugacity, we observe a phase transition with a two-dimensional Ising critical point. Above the transition point, the system is in an ordered state, with the majority of particles being either horizontally or vertically aligned. In contrast to previous work, we identify the transition as being of the liquid-gas type, as opposed to isotropic-to-nematic. This interpretation naturally accounts for the observed Ising critical behavior. Furthermore, when the Zwanzig fluid is extended to more allowed particle orientations, we argue that in some cases the symmetry of a q-state Potts model with q>2 arises. This observation is used to interpret a number of previous results.