Lee Song Sub, Kim Beom Jun
Department of Physics, Sungkyunkwan University, Suwon 16419, Republic of Korea.
Phys Rev E. 2019 Apr;99(4-1):043308. doi: 10.1103/PhysRevE.99.043308.
Thanks to the development of machine learning techniques, it has been shown that the supervised learning can be useful to study critical phenomena of various systems. However, the supervised learning cannot be done without labels which require knowledge about critical behavior of the system. To overcome this barrier, unsupervised machine learning methods have been considered and the confusion scheme has been proposed. In this study, we use the confusion scheme of the unsupervised learning and investigate critical behavior of various systems which exhibit single (double) phase transitions with (without) quasi-long-range order. In detail, we choose the two-color Ashkin-Teller model, the XY model, and the eight-state clock model as such systems and snapshots of the spin configurations at various temperatures are collected via Monte Carlo simulations to be used as input data for the unsupervised machine learning. We also put focus on the size dependence of results and validate the availability of the confusion scheme in thermodynamic limit. Our results indicate that the confusion scheme of the unsupervised learning successfully locates the approximate transition points for all models and becomes more accurate as the system size is increased. We also find a characteristic feature of the result which reflects the presence of a quasi-long-range order. We conclude that regardless of the presence of a quasi-long-range order, single and double phase transitions can be detected via the confusion scheme.
得益于机器学习技术的发展，研究表明监督学习对于研究各种系统的临界现象可能是有用的。然而，没有标签就无法进行监督学习，而标签需要有关系统临界行为的知识。为了克服这一障碍，人们考虑了无监督机器学习方法并提出了混淆方案。在本研究中，我们使用无监督学习的混淆方案，研究各种表现出具有（不具有）准长程序的单（双）相变的系统的临界行为。具体而言，我们选择双色阿什金 - 泰勒模型、XY模型和八态时钟模型作为此类系统，并通过蒙特卡罗模拟收集不同温度下自旋构型的快照，用作无监督机器学习的输入数据。我们还关注结果的尺寸依赖性，并在热力学极限下验证混淆方案的有效性。我们的结果表明，无监督学习的混淆方案成功地找到了所有模型的近似转变点，并且随着系统尺寸的增加变得更加准确。我们还发现了结果的一个特征，它反映了准长程序的存在。我们得出结论，无论是否存在准长程序，都可以通过混淆方案检测单双相变。
