机器学习识别六方伊辛晶格中的相位和相变

Phases and Phase Transitions in Hexagonal Ising Lattices Identified by Machine Learning

摘要: 机器学习可以在对系统潜在特性缺乏先验知识的情况下，识别数据中的模式并发现物理系统的性质和物理量。在本文中，我们使用非监督机器学习技术——主成分分析(Principal Component Analysis, PCA)方法识别六方伊辛晶格的相和相变。研究表明，PCA可以成功识别六方伊辛晶格的相变并定位相变临界温度。此外，通过PCA所获得的第一和第二主成分还可用于确定晶格的磁化强度和磁化率。

Abstract: Machine learning can identify patterns in data and discover the properties and physical quantities of physical systems without prior knowledge of the system’s latent characteristics. In this paper, we employ unsupervised machine learning techniques—specifically, Principal Component Analysis (PCA)—to identify the phases and phase transitions of the hexagonal Ising lattice. Our study demonstrates that PCA can successfully identify the phase transitions of the hexagonal Ising lattice and locate the critical temperature of these transitions. Furthermore, the first and second principal components obtained through PCA can also be used to determine the lattice's magnetization and susceptibility.