Allen-Cahn（模型A）类中的相序动力学：通过液晶中电致相变阐明的普适特性
Phase-ordering kinetics in the Allen-Cahn (Model A) class: universal aspects elucidated by electrically-induced transition in liquid crystals
AI总结：
本研究利用二维扭曲向列液晶的电致超快相变实验，验证了Allen-Cahn（模型A）类相序动力学的多种标度理论，修正了部分理论预测，为非平衡系统普适性研究提供了实验原型。
摘要：
二维（2d）伊辛模型是统计物理中关于相变及其动力学的经典教科书案例。通过Glauber速率在居里点以下淬灭时，铁磁畴粗化的晚期描述属于Allen-Cahn（模型A）类的标量分支。自1962年Lifshitz的研究以来，二维模型A的核心物理量——大多数标度指数和关联函数——一直缺乏精确结果，现有近似理论的结果差异很大，亟需实验验证。\n本文通过对二维扭曲向列液晶粗化过程的综合研究开展了此类实验验证，其动力学由超快切换驱动：从时空混沌态转变为两相共存的平衡态。我们通过光学显微镜追踪动力学过程，首先给出了模型A已有特性的明确证据，例如动力学指数$z=2$和动力学标度假设，随后开展了进一步研究。\n我们证实了描述空间关联函数畴内长度标度的Porod区的Bray-Humayun理论，并表明超出该区的非平凡衰减可以由高斯理论以无参数的方式准确描述。然而，这些经典理论在模型A的时间相关统计量上表现不佳。我们发现，两次关联函数的塌缩形式可以由局域标度不变性理论结合Fisher-Huse猜想最好地解释。我们还给出了局域 persistence 指数的真实取值，该结果不支持高斯模型，并提取了persistence团簇形态的普适分形维数，该值显著接近黄金分割比。鉴于其精度和应用潜力，该实验装置可作为研究非平衡系统领域普适性问题的原型平台。
英文摘要：
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.
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