Temperature-conditioned deep generative framework for scalable Ising spin configuration synthesis with...

Area of Science:

• Statistical Mechanics
• Computational Physics
• Machine Learning

Background:

• The 2D Ising model is a fundamental model in statistical mechanics for understanding magnetism and phase transitions.
• Generating accurate spin configurations is computationally intensive, especially for large systems or near critical points.
• Deep generative models offer potential for efficient and scalable simulation of physical systems.

Purpose of the Study:

• To develop a temperature-conditioned deep generative approach for efficient spin configuration generation in the 2D Ising model.
• To ensure physical consistency and thermodynamic accuracy of generated configurations.
• To provide a scalable method for creating synthetic data for further analysis of phase transitions.

Main Methods:

• A convolutional generator network conditioned on spin states, temperature, and noise was employed.
• Physics-based constraints (magnetization, energy, correlations) were integrated as auxiliary loss terms.
• Monte Carlo simulations were used to derive baseline data and constraints for training.

Main Results:

• The model generated thermodynamically accurate spin configurations, closely matching Monte Carlo baselines across various lattice sizes (L=16, 32, 64).
• Mean absolute errors were as low as 0.0016 for magnetization and correlation, and 0.0063 for energy at L=64.
• Generated data enabled accurate phase classification, with F1 scores above 0.99 using ensemble classifiers.

Conclusions:

• The proposed deep generative framework offers a computationally efficient and scalable solution for generating 2D Ising model spin configurations.
• This method accurately captures critical phenomena and provides high-quality synthetic data for physical system analysis.
• The approach demonstrates the power of integrating physics-based constraints into deep learning for scientific simulation.