InfoCGAN classification of 2D square Ising configurations

Abstract

An InfoCGAN neural network is trained on 2D 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. Proper implementation of finite size scaling is essential for a complete machine learning approach in order to bring it in line with established statistical mechanics, which is worthwhile for future study.