Title: Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders,
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.