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

Giovanni De Matteis, Francesco Giglio*, Antonio Moro

*Corresponding author for this work

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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 analogue. 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.
Original languageEnglish
Article number20230701
Pages (from-to)1-27
Number of pages27
JournalProceedings of the Royal Society A
Volume480
Issue number2283
DOIs
Publication statusPublished - 14 Feb 2024

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