Incremental learning of phase transition in Ising model: Preprocessing, finite-size scaling and critical exponents

Abstract

We investigated an unsupervised machine learning to recognize the phase transition in Ising model by using principal component analysis (PCA) with a preprocessing of raw data, and we realized the large-scale calculations and finite-size scaling analysis based on the incremental PCA. It was shown that the two different phases are clearly and reasonably recognized by the k-means clustering of the first and second principal components. Taking the normalized first principal component as the order parameter, we calculated the critical properties near the phase transition point by using the finite-size scaling method. Our results of the critical temperature and critical exponents are consistent with the classical values, which indicates that the first principal component is capable of catching main features of the phase transition. The present scheme provides an alternative way with emphasis on data preprocessing and incremental PCA for the unsupervised machine learning of the phase transition in Ising model and its related spin models.