Generating the Critical Ising Model via SRGAN: A Schramm–Loewner Evolution Analysis from a Geometric Deep Learning Perspective

The geometric signatures of macroscopic interfaces in the two-dimensional critical Ising model strictly adhere to Schramm–Loewner Evolution (SLE) theory. In this study, we propose a physics-driven generative approach using Super-Resolution Generative Adversarial Networks (SRGANs) to approximate the inverse coarse-graining operation to generate larger configurations. From the perspective of Geometric Deep Learning (GDL), we leverage the geometric priors of Convolutional Neural Networks (CNNs)—specifically their translational and rotational symmetries—to effectively encode the universal physical laws of the Ising Hamiltonian. This inductive bias allows the model to be trained on small scales yet be generalized to large-scale systems (2048×2048) while preserving physical conservation. To accommodate spin discreteness, we employ an L1-based loss function to maintain domain wall sharpness. SLE analysis and long-range correlation functions confirm that the model reproduces critical dynamics and conformal invariance, successfully serving as a physics-preserving inverse coarse-graining transformation framework.