发表机构
Indian Institute of Technology Kanpur; KU Leuven（坎普尔印度理工学院; 荷语鲁汶大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出基于GMM的标量势，兼具自旋模型的易采样性与目标理论的临界性质，构建了多种对称情形的模型并验证二维Z₂对称属于伊辛普适类。
AI 中文摘要
具有给定对称性的自旋模型在格点上比相同对称性的标量理论更易采样，因为自旋变量的约束特性可实现廉价的热浴更新。但这种约束会抑制径向涨落，因此自旋模型无法用于研究自发对称破缺现象，如希格斯现象。为解决该问题，我们提出一类基于高斯混合模型（GMM）的标量势，其采样难度与具有给定对称性的自旋模型相当。这些势可被设计为属于目标理论的同一普适类，从而重现其临界性质并实现高效采样。我们针对全局$\boldsymbol{\text{Z}}_2$对称性、$\text{U}(1)$规范对称性及无序系统构建此类模型，还通过数值实验验证，二维$\text{Z}_2$对称性情形属于二维伊辛普适类。
英文摘要
Spin models with a given symmetry are easier to sample than scalar theories with the same symmetry on a lattice, as the constrained nature of spin variables enables cheap heat-bath updates. However, this constraint suppresses radial fluctuations, and consequently, spin models cannot be used to study the phenomena of spontaneous symmetry breaking, such as the Higgs phenomenon. To address this, we propose a class of scalar potentials based on Gaussian Mixture Models (GMMs) that are as easy to sample as spin models with a given symmetry. These potentials can be designed to belong to the same universality class as the theory of interest, thereby reproducing its critical properties while enabling efficient sampling. We construct such models for global $\mathbb{Z}_2$ symmetry, $U(1)$ gauge symmetry, and disordered systems. We also verify by numerical experiment that the case of $\mathbb{Z}_2$ symmetry in two dimensions lies in the two-dimensional Ising universality class.
Comments10 Pages, 7 figures
