由微观自由度观测反演格点模型：用不确定性量化进行参数估计
Inversion of lattice models from the observations of microscopic degrees of freedom: parameter estimation with uncertainty quantification
摘要：
凝聚态物理和材料科学的实验进展已经使人们能够随时获得原子分辨率的图像，现代工具的分辨率通常足以提取破坏对称性的扭曲的微小细节，如偏振、八面体倾斜或其他结构耦合的序参量。观察到的变形模式反过来包含了微观驱动力的信息，定义了材料微观结构和相关热力学的发展。然而，从实验观察到的微观自由度的基础物理模型的分析仍然是一个基本上悬而未决的问题。在这里，我们探索这样一种方法使用的范式伊辛模型的正方形晶格。我们表明，微观参数的伊辛模型的铁磁和反铁磁的情况下，可以提取的自旋配置的温度高于一个数量级的相变，并进行不确定性分析，这样的重建。这表明，对材料进行足够高精度的显微观察可以在远高于相应相变的温度下提供有关生成物理学的信息，通过高分辨率成像为科学探索开辟新的视野。
英文摘要：
Experimental advances in condensed matter physics and material science have enabled ready access to atomic-resolution images, with resolution of modern tools often sufficient to extract minute details of symmetry-breaking distortions such as polarization, octahedra tilts, or other structure-coupled order parameters. The patterns of observed distortions in turn contain the information on microscopic driving forces defining the development of materials microstructure and associated thermodynamics. However, the analysis of underpinning physical models from experimentally observed microscopic degrees of freedom remains a largely unresolved issue. Here, we explore such an approach using the paradigmatic Ising model on a square lattice. We show that the microscopic parameters of the Ising model both for ferromagnetic and antiferromagnetic case can be extracted from the spin configurations for temperatures an order of magnitude higher than the phase transition and perform uncertainty analysis for such reconstructions. This suggests that microscopic observations of materials with sufficiently high precision can provide information on generative physics at temperatures well above corresponding phase transition, opening new horizons for scientific exploration via high-resolution imaging.
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