SUPPLEMENTARY INFORMATION

The supplementary material document for this publication provides additional details on the Ginzburg-Landau-Devonshire (LGD) thermodynamic model used to describe the physical system (S1), the derivation of the linearized equations relating observable and non-observable variables (S2-S3), and a comprehensive listing of the phenomenological parameters and correlation lengths used in the calculations (Tables SI-SII). It also includes a dedicated section (S4) outlining the specific data pre-requirements and optimal conditions for applying the LiNGAM model to experimental STEM data.