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.