临界现象数值研究中Bootstrap方程的自动生成
An Automated Generation of Bootstrap Equations for Numerical Study of Critical Phenomena
摘要：
在这篇论文中，我们介绍了新的工具，共形引导，autoboot和qboot。每个工具解决了一个不同的步骤，在整个计算栈，并结合现有的高效工具SDPB解决半定规划（SDP），我们的工具，使它更容易研究共形场论更复杂的全球对称性和更一般的频谱。在引言中，我们回顾了共形引导方法是如何在重整化群的不动点处给出理论的丰富信息的，或者换句话说，在临界处的临界现象，如伊辛模型。以下三个部分重点介绍autoboot和qboot实现背后的理论，第5部分讨论了在https://github.com/selpoG/autoboot/和https：//github.com/selpoG/qboot/上免费提供的显式实现。在最后一节中我们还介绍了两个应用，伊辛模型和O（2）矢量模型，它们都与现实世界中的物理系统有着密切的联系。
英文摘要：
In this thesis, we introduce new tools for the conformal bootstrap, autoboot and qboot. Each tool solves a different step in the whole computational stack, and combined with an existing efficient tool SDPB which solves semidefinite programming (SDP), our tools make it easier to study conformal field theories with more complicated global symmetries and with more general spectra. In the introduction, we review how the conformal bootstrap method gives rich information about the theory at the fixed point of renormalization group, or in other words, the critical phenomena such as the Ising model at criticality. The following three sections focus on the theories behind the implementation of autoboot and qboot, and the explicit implementation, freely available at https://github.com/selpoG/autoboot/ and https://github.com/selpoG/qboot/, is discussed in section 5. We also have two applications in the last section, the Ising model and the O(2) vector model in three dimensions, each of them has close relationship with a physical system in the real world.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
