Phase-ordering kinetics in the Allen-Cahn (Model A) class: Universal aspects elucidated by electrically induced transition in liquid crystals
Phase-ordering kinetics in the Allen-Cahn (Model A) class: Universal aspects elucidated by electrically induced transition in liquid crystals
复制标题
Allen-Cahn（模型 A）类中的相序动力学：液晶中电诱导转变阐明的普遍方面
DOI：
10.1103/physreve.104.054103
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发表时间：
2021
影响因子：
2.4
通讯作者：
Takeuchi Kazumasa A.
中科院分区：
文献类型：
--
作者：
Almeida Renan A. L.;Takeuchi Kazumasa A.
二维 (2D) 伊辛模型是相变及其动力学的统计物理教科书示例。通过格劳伯率淬灭通过居里点，铁磁畴粗化的后期描述在 Allen-Cahn（或模型 A）类的标量扇区中找到了自己的位置，其中包含赋予非守恒有序参数的相序动力学。自 1962 年 Lifshitz 首次提出理论以来，理论家们一直在寻求精确结果，但 2D 模型 A 的核心量（大多数标度指数和相关函数）仍然是已知的近似理论，其不同的结果需要实验评估。在这里，我们基于对二维扭曲向列液晶粗化的综合研究来进行这种评估，其动力学是由从时空混沌（无序）状态到两相并发平衡状态的超快电切换引起的。通过光学显微镜跟踪动力学，我们首先展示了已建立的模型 A 方面的尖锐证据，例如动态指数和动态缩放假设，然后继续前进。我们证实了描述两点空间相关器域内长度尺度的波罗德体系的布雷-胡马云理论，并表明它们超出波罗德尺度的非平凡衰变可以通过高斯理论（即 Ohta-Jasnow-Kawasaki (OJK) 和 Mazenko 理论）以无参数的方式捕获。关于与时间相关的统计数据，我们证实了模型 A 系统中的老化假设，其中包括将两次相关器折叠成一条主曲线，其格式实际上最好由局部标度不变性理论的解来解释：该解与二维非保守伊辛模型相关器以及 Fisher-Huse 猜想相吻合。我们还建议模型 A 类中局部持续指数的真实值，而不利于扩散和 OJK 方程的确切结果。最后，我们观察持久性簇的分形形态并提取它们的通用维数。鉴于其准确性和可能性，该实验装置可以作为原型来解决非平衡系统领域的进一步普遍性问题。
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 (or Model A) class, which encompasses phase-ordering kinetics endowed with a nonconserved order parameter. Resisting exact results sought for theoreticians since Lifshitz's first account in 1962, the central quantities of 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 based on a comprehensive study of the coarsening of 2D twisted nematic liquid crystals whose kinetics is induced by a superfast electrical switching from a spatiotemporally chaotic (disordered) state to a two-phase concurrent, equilibrium one. Tracking the dynamics via optical microscopy, we first show the sharp evidence of well-established Model A aspects, such as the dynamic exponentand the dynamic scaling hypothesis, to then move forward. We confirm the Bray-Humayun theory for Porod's regime describing intradomain length scales of the two-point spatial correlators and show that their nontrivial decay beyond the Porod's scale can be captured in a free-from-parameter fashion by Gaussian theories, namely the Ohta-Jasnow-Kawasaki (OJK) and Mazenko theories. Regarding time-related statistics, we corroborate the aging hypothesis in Model A systems, which includes the collapse of two-time correlators into a master curve whose format is, actually, best accounted for by a solution of the local scaling invariance theory: the same solution that fits the 2D nonconserved Ising model correlator along with the Fisher-Huse conjecture. We also suggest the true value for the local persistence exponent in Model A class, in disfavor of the exact outcome for the diffusion and OJK equations. Finally, we observe a fractal morphology for persistence clusters and extract their universal dimension. Given its accuracy and possibilities, this experimental setup may work as a prototype to address further universality issues in the realm of nonequilibrium systems.