# Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders

## TL;DR

This paper demonstrates that unsupervised machine learning methods, including PCA and variational autoencoders, can identify phase transitions and order parameters in statistical physics models without prior knowledge.

## Contribution

It introduces the use of neural network-based autoencoders to detect phase transitions and order parameters in Ising and XY models, extending previous PCA-based approaches.

## Key findings

- Latent parameters match known order parameters.
- States form clusters indicating phases.
- Reconstruction loss signals phase transitions.

## Abstract

We employ unsupervised machine learning techniques to learn latent parameters which best describe states of the two-dimensional Ising model and the three-dimensional XY model. These methods range from principal component analysis to artificial neural network based variational autoencoders. The states are sampled using a Monte-Carlo simulation above and below the critical temperature. We find that the predicted latent parameters correspond to the known order parameters. The latent representation of the states of the models in question are clustered, which makes it possible to identify phases without prior knowledge of their existence or the underlying Hamiltonian. Furthermore, we find that the reconstruction loss function can be used as a universal identifier for phase transitions.