De Matteis, G., Giglio, F. and Moro, A. (2024) Complete integrability and equilibrium thermodynamics of biaxial nematic systems with discrete orientational degrees of freedom. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 480(2283), 20230701. (doi: 10.1098/rspa.2023.0701)
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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 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.
| Item Type: | Articles |
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| Additional Information: | We would like to thank the Isaac Newton Institute for Mathematical Sciences for the hospitality during the six-month programme ‘Dispersive hydrodynamics: mathematics, simulation and experiments, with applications in nonlinear waves’, Cambridge July-December 2022, under the EPSRC Grant Number EP/R014604/1, where this work has been partly developed, and GNFM - Gruppo Nazionale per la Fisica Matematica, INdAM (Istituto Nazionale di Alta Matematica). F.G. also acknowledges the hospitality of the Department of Mathematics, Physics and Electrical Engineering of Northumbria University Newcastle. A.M. is supported by the Leverhulme Trust Research Project Grant 2017-228, the Royal Society International Exchanges Grant IES-R2-170116 and London Mathematical Society. |
| Keywords: | Liquid crystals, integrability, phase transitions, biaxiality. |
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Giglio, Dr Francesco |
| Creator Roles: | Giglio, F.Conceptualization, Formal analysis, Funding acquisition, Investigation, Methodology, Resources, Validation, Visualization, Writing – original draft, Writing – review and editing |
| Authors: | De Matteis, G., Giglio, F., and Moro, A. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |
| Publisher: | The Royal Society |
| ISSN: | 1364-5021 |
| ISSN (Online): | 1471-2946 |
| Published Online: | 14 February 2024 |
| Copyright Holders: | Copyright © 2024 The Authors |
| First Published: | First published in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 480(2283):20230701 |
| Publisher Policy: | Reproduced under a Creative Commons license |
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