AI 中文总结
该研究提出重正化群引导逆阻塞算法，结合条件归一化流与再热化实现格点场生成，在二维φ⁴理论中完成16²至2048²格点的稳定级联上采样，具备高维系统扩展潜力。
AI 中文摘要
我们提出一种基于重正化群阻塞变换近似逆变换的格点场构型生成算法。我们采用“完美阻塞”条件优化阻塞变换，使阻塞后的格点分布能被简单的粗粒化作用良好近似。该阻塞过程分为可逆平滑变换与抽取两步，采用条件归一化流（conditional normalizing flow）形式的机器学习方法重构抽取过程中被移除的短程自由度，再通过短程精细作用的再热化消除残留失配。由于粗粒化系综提供长程模式，相同的阻塞变换与条件流可在更大格点上递归复用，从小体积初始系综生成级联构型。我们在临界态下的二维φ⁴理论（λ=1）中测试该方法，在本地计算资源上实现从16²到2048²格点的稳定级联上采样。可控再热化测试显示，短程失配快速弛豫，而在相关热方向刻意引入的失配则弛豫缓慢。该构建方法的组成部分可自然扩展至高维系统，最终可应用于规范和费米子自由度。
英文摘要
We propose an algorithm for generating lattice field configurations based on the approximate inversion of a renormalization-group blocking transformation. We optimize the blocking transformation using a ``perfect blocking'' condition so that the blocked lattice distribution is well approximated by a simple coarse action. The blocking is separated into an invertible smoothing transformation followed by decimation. Machine learning, in the form of a conditional normalizing flow, is used to reconstruct the short-distance degrees of freedom removed by the decimation. A short fine-action rethermalization then removes the residual mismatch. Because the coarse ensemble supplies the long-distance modes, the same blocking transformation and conditional flow can be reused recursively on larger lattices, producing a cascade of configurations from an initial small-volume ensemble. We test the method in two-dimensional $ϕ^4$ theory with $λ=1$ at criticality and demonstrate stable cascade upscaling from $16^2$ to $2048^2$ lattices on local computational resources. Controlled rethermalization tests show that short-distance mismatches relax rapidly, whereas a deliberately introduced mismatch in the relevant thermal direction relaxes much more slowly. The construction uses ingredients that admit natural extensions to higher-dimensional systems and, ultimately, to gauge and fermionic degrees of freedom.
Comments24 pages, 15 figures. Submitted to Phys. Rev. D
