用扩散模型加速连续自旋系统的热化，大幅缩短采样时间。
Diffusion-warm sampling of the XY model enables fast thermalization at scale
- 训练小尺度XY模型的温度条件扩散模型，生成大尺度准确样本。
- 结合少量MCMC步骤，热化时间比传统方法快一个数量级。
- 适合研究大规模连续自旋系统，对凝聚态物理有实用价值。
我们提出一种基于扩散模型的新型可扩展自旋系统采样技术，用于具有连续对称性的系统。以凝聚态物理中的基础模型XY模型为例，证明该方法克服了马尔可夫链蒙特卡洛（MCMC）在不同系统尺寸间泛化能力不足的问题。具体而言，在小尺寸XY晶格上训练温度条件扩散模型后，可在更大晶格尺寸生成高精度样本。通过追踪自旋关联等物理可观测量，实验表明，扩散采样结合少量MCMC步骤，使热化时间相比标准随机初始化的MCMC减少一个数量级。本研究为生成模型在大规模连续状态凝聚态系统中的应用提供了重要洞见。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。