格点场论中相变的数值研究
Numerical Investigations of Phase Transitions in Lattice Field Theories
- Indian Institute of Science Education & Research (IISER) Mohali（印度科学教育与研究学院莫哈利分校）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文通过GPU加速的HOTRG方法研究二维广义XY模型相图，并开发基于格点作用梯度和海森矩阵的构型温度估计器，用于验证热采样和诊断采样病态。
AI中文摘要：
相变的研究在理解物理系统在临界点行为发生定性变化方面起着重要作用。尽管经过数十年的进展，仍然迫切需要能够解析细微临界现象的高精度数值工具。基于这一需求，在本论文中，我们提出了对格点系统中相变的两个互补的数值研究。第一个研究使用GPU加速的高阶张量重正化群（HOTRG）技术来研究二维广义XY模型，表征其铁磁、向列和顺磁相，并使用热力学极限中的热力学观测量绘制其相边界。第二个研究开发并基准测试了一种构型温度估计器，该估计器由欧几里得格点作用的梯度和海森矩阵构建，应用于紧致U(1)格点规范理论。一方面，当截断和有限键效应得到充分控制时，张量网络方法能够捕捉丰富的相结构。另一方面，构型温度估计器提供了一种独立的、低开销的手段来验证不同算法和模型的热采样，并且还可以用作运行时诊断，在大规模生产运行之前识别采样病态。
英文摘要：
The study of phase transitions plays an important role in understanding qualitative changes in the behaviour of physical systems at criticality. Despite decades of progress, there is still a strong demand for high-precision numerical tools capable of resolving subtle critical phenomena. Motivated by this need, in this thesis, we present two complementary numerical investigations of phase transitions in lattice systems. The first uses GPU-accelerated higher-order tensor renormalization group (HOTRG) techniques to study the two-dimensional generalized XY model, characterizing its ferromagnetic, nematic, and paramagnetic phases and mapping their phase boundaries using thermodynamic observables in the thermodynamic limit. The second develops and benchmarks a configurational temperature estimator, constructed from gradients and Hessians of the Euclidean lattice action, in compact U(1) lattice gauge theories. On one hand, tensor network methods capture rich phase structures when truncation and finite-bond effects are adequately controlled. On the other hand, the configurational temperature estimator provides an independent, low-overhead means of validating thermal sampling across different algorithms and models, and can also be used as a runtime diagnostic to identify sampling pathologies before large-scale production runs.
