Temperature-conditioned deep generative framework for scalable Ising spin configuration synthesis with physics-informed constraints

This study presents a temperature-conditioned deep generative approach for efficiently generating spin configurations of the two-dimensional (2D) Ising model. The method employs a convolutional generator network, conditioned on spin states, temperature embeddings, and random noise, to generate thermodynamically accurate spin configurations on a 2D square lattice. Physics-based constraints, derived from magnetization, energy, and nearest-neighbor correlations obtained via Monte Carlo simulations, are integrated as auxiliary loss terms during training to ensure physical consistency. The model accurately captures phase transition behaviors near the critical temperature and supports the scalable generation of synthetic configurations for further analysis. Investigations across lattice sizes L=16, 32, and 64 demonstrate close alignment with Monte Carlo baselines, with generated configurations achieving mean absolute errors as low as 0.0016 for magnetization, 0.0063 for energy, and 0.0016 for correlation in the L=64 case. Phase classification using standard machine learning models further validates the quality of the generated data, with ensemble classifiers yielding F1 scores above 0.99. These findings highlight the proposed framework as a scalable, computationally efficient solution for generating spin configurations in an Ising model.