通过学习多尺度采样克服阻挫自旋系统中的临界慢化
Overcoming critical slowing down in frustrated spin systems by learned multiscale sampling
- SISSA — International School for Advanced Studies and INFN（国际高等研究学院和意大利国家核物理研究所）
- Laboratoire de Physique Statistique, École normale supérieure, PSL Research University（巴黎高等师范学院统计物理实验室，PSL研究大学）
- Department of Physics, Duke University（杜克大学物理系）
- Department of Chemistry, Duke University（杜克大学化学系）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究采用小波条件重整化群（WCRG）采样方法学习多尺度采样，克服了传统集团算法失效的阻挫自旋系统临界慢化问题，采样复杂度达O(log₂L)，精度取决于能量基模型的表达能力。
AI中文摘要：
Swendsen-Wang和Wolff等集团算法是缓解统计系统中临界慢化最成功的MCMC方法，但这类构造性集团算法在存在极弱阻挫时就会失效。本文通过学习而非构造相关集团来规避这一根本局限，具体采用小波条件重整化群（WCRG）采样方法学习二维阻挫软自旋模型的集体涨落概率分布，随后通过从粗尺度到细尺度采样条件小波分布递归生成构型。WCRG方法可复现系统在不同相的主要统计性质，包括局域场分布和结构因子；在类伊辛临界点，条件动力学在每个尺度的O(1)次扫描内保持去相关，整体采样复杂度为O(log₂L)，远优于标准局部MCMC方法。这些结果表明，学习多尺度采样可克服传统集团算法失效的阻挫系统临界慢化；通过评估不同可观测量的采样精度，还明确了WCRG方法的主要权衡：快速采样方案的精度取决于用于估计小波条件分布的能量基模型的表达能力。
英文摘要：
Cluster algorithms, such as the Swendsen--Wang and Wolff methods, are among the most successful MCMC methods for mitigating critical slowing down in statistical systems. These constructive cluster algorithms, however, fail in the presence of even extremely weak frustration. Here, we sidestep this fundamental limitation by learning rather than constructing the relevant clusters. Specifically, we use the wavelet conditional renormalization group (WCRG) sampling method to learn the probability distribution of collective fluctuations of a frustrated two-dimensional soft-spin model. Configurations are then generated recursively from coarse to fine scales by sampling conditional wavelet distributions. The WCRG method reproduces the main statistical properties of the system across different phases, including the local-field distribution and the structure factor. At an Ising-like critical point, the conditional dynamics remains decorrelated within $\mathcal{O}(1)$ sweeps at each scale, yielding an overall sampling complexity of $\mathcal{O}(\log_2 L)$, thus making WCRG much more efficient than standard local MCMC methods. These results show that learned multiscale sampling can overcome critical slowing down in frustrated systems for which conventional cluster algorithms fail. By assessing the sampling accuracy of different observables, we also clarify the main tradeoff of the WCRG method: the accuracy of the fast sampling scheme depends on the expressiveness of the energy-based model used to estimate the wavelet conditional distributions.
