Theory and simulation of two-dimensional nematic and tetratic phases

TL;DR

This paper develops a theoretical and computational framework to understand how two-dimensional particles with near four-fold symmetry can form tetratic phases, despite weak symmetry breaking, supported by phase diagram calculations and Monte Carlo simulations.

Contribution

It introduces a model for particles with nearly four-fold symmetry, derives a mean-field phase diagram, and validates it with Monte Carlo simulations, bridging theory and computational results.

Findings

Tetratic phase persists despite significant symmetry breaking.

Mean-field phase diagram aligns with previous models.

Monte Carlo simulations confirm theoretical predictions.

Abstract

Recent experiments and simulations have shown that two-dimensional systems can form tetratic phases with four-fold rotational symmetry, even if they are composed of particles with only two-fold symmetry. To understand this effect, we propose a model for the statistical mechanics of particles with almost four-fold symmetry, which is weakly broken down to two-fold. We introduce a coefficient $\kappa$ to characterize the symmetry breaking, and find that the tetratic phase can still exist even up to a substantial value of $\kappa$. Through a Landau expansion of the free energy, we calculate the mean-field phase diagram, which is similar to the result of a previous hard-particle excluded-volume model. To verify our mean-field calculation, we develop a Monte Carlo simulation of spins on a triangular lattice. The results of the simulation agree very well with the Landau theory.