Complete integrability and equilibrium thermodynamics of biaxial nematic systems with discrete orientational degrees of freedom

TL;DR

This paper presents an exactly solvable discrete biaxial nematic liquid crystal model, deriving its free energy and phase diagram, revealing complex phase transitions and demonstrating the model's relevance to continuum systems.

Contribution

The paper introduces a new discrete model for biaxial nematic systems with exact solutions, connecting discrete and continuum descriptions.

Findings

Exact free energy and equations of state derived

Rich phase diagram with multiple phase transitions identified

Discrete model results align qualitatively with continuum models

Abstract

We study a discrete version of a biaxial nematic liquid crystal model with external fields via an approach based on the solution of differential identities for the partition function. In the thermodynamic limit, we derive the free energy of the model and the associated closed set of equations of state involving four order parameters, proving the integrability and exact solvability of the model. The equations of state are specified via a suitable representation of the orientational order parameters, which imply two-order parameter reductions in the absence of external fields. A detailed exact analysis of the equations of state reveal a rich phase diagram where isotropic versus uniaxial versus biaxial phase transitions are explicitly described, including the existence of triple and tricritical points. Results on the discrete models are qualitatively consistent with their continuum analog. This observation suggests that, in more general settings, discrete models may be used to capture and describe phenomena that also occur in the continuum for which exact equations of state in closed form are not available.