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

Area of Science:

• Statistical Physics
• Machine Learning
• Computational Physics

Background:

• Macroscopic interfaces in 2D critical Ising models follow Schramm-Loewner Evolution (SLE) theory.
• Inverse coarse-graining is crucial for generating large-scale physical system configurations.

Purpose of the Study:

• To propose a physics-driven generative approach for inverse coarse-graining.
• To leverage Geometric Deep Learning (GDL) and Super-Resolution Generative Adversarial Networks (SRGANs) for generating large Ising model configurations.

Main Methods:

• Utilized SRGANs for inverse coarse-graining.
• Employed Convolutional Neural Networks (CNNs) with geometric priors (translational and rotational symmetries).
• Applied an L1-based loss function to maintain domain wall sharpness for discrete spins.

Main Results:

• Generated large-scale (2048 × 2048) Ising model configurations while preserving physical conservation.
• Demonstrated that the model generalizes from small to large scales due to inductive bias.
• SLE analysis and correlation functions confirmed reproduction of critical dynamics and conformal invariance.

Conclusions:

• The SRGAN-based framework successfully serves as a physics-preserving inverse coarse-graining transformation.
• This approach effectively encodes universal physical laws of the Ising Hamiltonian.
• The method validates the application of GDL in simulating critical phenomena.