Construction of phase diagrams of spin models using unsupervised machine learning

Yutaka Akagi, Nobuyuki Yoshioka, Hosho Katsura

Joaquin F. Rodriguez-Nieva, Mathias S. Scheurer

Wei Yu, Pin Lyu

Danilo Rodrigues de Assis Elias

Nan Wu, Zhuohan Li, Wanzhou Zhang

In recent years, developing unsupervised machine learning for identifying phase transition is a research direction. In this paper, we introduce a two-times clustering method that can help select perfect configurations from a set of degenerate samples and assign the configuration with labels in a manner of unsupervised machine learning. These perfect configurations can then be used to train a neural network to classify phases. The derivatives of the predicted classification in the phase diagram, show peaks at the phase transition points. The effectiveness of our method is tested for the Ising, Potts, and Blume-Capel models. By using the ordered configuration from two-times clustering, our method can provide a useful way to obtain phase diagrams.

Santiago Acevedo, Marcelo Arlego, Carlos Alberto Lamas

We apply unsupervised learning techniques to classify the different phases of the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ antiferromagnetic Ising model on the honeycomb lattice. We construct the phase diagram of the system using convolutional autoencoders. These neural networks can detect phase transitions in the system via ``anomaly detection'' without the need for any label or a priori knowledge of the phases. We present different ways of training these autoencoders, and we evaluate them to discriminate between distinct magnetic phases. In this process, we highlight the case of high-temperature or even random training data. Finally, we analyze the capability of the autoencoder to detect the ground state degeneracy through the reconstruction error.