  An InfoCGAN neural network is trained on 2-dimensional square Ising
configurations conditioned on the external applied magnetic field and the
temperature. The network is composed of two main sub-networks. The generator
network learns to generate convincing Ising configurations and the
discriminator network learns to discriminate between "real" and "fake"
configurations with an additional categorical assignment prediction provided by
an auxiliary network. Some of the predicted categorical assignments show
agreement with the expected physical phases in the Ising model, the
ferromagnetic spin-up and spin down phases as well as the high temperature weak
external field phase. Additionally, configurations associated with the
crossover phenomena are predicted by the model. The classification
probabilities allow for a robust method of estimating the critical temperature
in the vanishing field case, showing exceptional agreement with the known
physics. This work indicates that a representation learning approach using an
adversarial neural network can be used to identify categories that strongly
resemble physical phases with no a priori information beyond raw physical
configurations and the physical conditions they are subject to.
