Diffusion-warm sampling of the XY model enables fast thermalization at scale
This work addresses the slow thermalization of MCMC for continuous-spin systems in condensed matter physics, offering a faster sampling method that scales to larger systems.
The paper introduces a diffusion model-based technique for sampling the XY model, achieving an order of magnitude reduction in thermalization time compared to standard MCMC when combined with a few MCMC steps, and enabling generalization to larger lattice sizes after training on smaller ones.
We introduce a novel technique for scalable sampling of spin-system states with continuous symmetries using diffusion models. By applying our approach to the XY model, a fundamental continuous-spin model in condensed matter physics, we show that our technique addresses the shortfalls of the Markov chain Monte Carlo (MCMC) in generalization to varying system sizes. More specifically, we show that training a temperature-conditioned diffusion model on smaller-size XY model lattices enables the generation of accurate samples in larger lattice sizes. By tracking physically important observables of the model, such as spin correlations, our experiments demonstrate that diffusion sampling followed by a few MCMC steps reduces the thermalization time by an order of magnitude relative to the standard MCMC with random initialization. Our study provides valuable insight as to how generative models can be used to study continuous-state condensed matter systems at scale.