Phase-ordering kinetics in the Allen-Cahn (Model A) class: universal aspects elucidated by electrically-induced transition in liquid crystals
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| Format: | Preprint |
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2021
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| _version_ | 1866929274241417216 |
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| author | Almeida, Renan A. L. Takeuchi, Kazumasa A. |
| author_facet | Almeida, Renan A. L. Takeuchi, Kazumasa A. |
| contents | The two-dimensional (2d) Ising model is the statistical physics textbook example for phase transitions and their kinetics. Quenched through the Curie point with Glauber rates, the late-time description of the ferromagnetic domain coarsening finds its place at the scalar sector of the Allen-Cahn (Model A) class. Resisting exact results sought since Lifshitz's account in 1962, central quantities in 2d Model A $-$ most scaling exponents and correlation functions $-$ remain known up to approximate theories whose disparate outcomes urge experimental assessment. Here, we perform such assessment from a comprehensive study of the coarsening of 2d twisted nematic liquid crystals whose kinetics is induced by a super-fast switching from a spatiotemporally chaotic state to a two-phase concurrent, equilibrium one. Tracking the dynamics via optical microscopy, we firstly show the sharp evidence of well-established Model A aspects, such as the dynamic exponent $z=2$ and the dynamic scaling hypothesis, to then move forward. We confirm the Bray-Humayun theory for Porod's regime describing intradomain length scales of spatial correlators, and show that their nontrivial decay beyond that regime is captured in a free-from-parameter fashion by Gaussian theories. These paradigmatic theories, however, do not perform well for time-related Model A statistics. We reveal that the collapsed form of two-time correlators is best accounted for by the local scaling invariance theory, along with the Fisher-Huse conjecture. We also suggest the true value for the local persistence exponent, in disfavour of Gaussian models, and extract a universal fractal dimension for the morphology of persistence clusters that is notably close to the golden ratio. Given its accuracy and possibilities, this experimental setup may work as a prototype to address universality issues in the realm of nonequilibrium systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2107_09043 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Phase-ordering kinetics in the Allen-Cahn (Model A) class: universal aspects elucidated by electrically-induced transition in liquid crystals Almeida, Renan A. L. Takeuchi, Kazumasa A. Statistical Mechanics Soft Condensed Matter The two-dimensional (2d) Ising model is the statistical physics textbook example for phase transitions and their kinetics. Quenched through the Curie point with Glauber rates, the late-time description of the ferromagnetic domain coarsening finds its place at the scalar sector of the Allen-Cahn (Model A) class. Resisting exact results sought since Lifshitz's account in 1962, central quantities in 2d Model A $-$ most scaling exponents and correlation functions $-$ remain known up to approximate theories whose disparate outcomes urge experimental assessment. Here, we perform such assessment from a comprehensive study of the coarsening of 2d twisted nematic liquid crystals whose kinetics is induced by a super-fast switching from a spatiotemporally chaotic state to a two-phase concurrent, equilibrium one. Tracking the dynamics via optical microscopy, we firstly show the sharp evidence of well-established Model A aspects, such as the dynamic exponent $z=2$ and the dynamic scaling hypothesis, to then move forward. We confirm the Bray-Humayun theory for Porod's regime describing intradomain length scales of spatial correlators, and show that their nontrivial decay beyond that regime is captured in a free-from-parameter fashion by Gaussian theories. These paradigmatic theories, however, do not perform well for time-related Model A statistics. We reveal that the collapsed form of two-time correlators is best accounted for by the local scaling invariance theory, along with the Fisher-Huse conjecture. We also suggest the true value for the local persistence exponent, in disfavour of Gaussian models, and extract a universal fractal dimension for the morphology of persistence clusters that is notably close to the golden ratio. Given its accuracy and possibilities, this experimental setup may work as a prototype to address universality issues in the realm of nonequilibrium systems. |
| title | Phase-ordering kinetics in the Allen-Cahn (Model A) class: universal aspects elucidated by electrically-induced transition in liquid crystals |
| topic | Statistical Mechanics Soft Condensed Matter |
| url | https://arxiv.org/abs/2107.09043 |