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Nanoscale probes often reveal complex, multiscale electronic structures at the surface of correlated quantum materials. Our resonant magnetic X-ray scattering nanoprobe measurements revealed a scale-free distribution of antiferromagnetic domains with fractal magnetic geometry [Li et al., Nat. Commun., 2019].  We use 4-state clock models to predict the expected shapes and statistics of these domains near the critical point.  Using cluster techniques, we compare the critical exponents from these models to the fractal magnetic textures observed with X-ray scattering in order to identify the critical point controlling the complex pattern formation.  We find that the critical exponents from the 2D Random Field 4-Clock Model are consistent with the critical exponents measured in NdNiO₃.