Simulating the Ising Model with a Deep Convolutional Generative Adversarial Network

Abstract: The deep learning framework is witnessing expansive growth into diverse applications such as biological systems, human cognition, robotics, and the social sciences, thanks to its immense ability to extract essential features from complicated systems. In particular, recent developments of the field have revealed the unique faculty of deep learning to accurately approximate complex physical systems in fluid dynamics, condensed matter physics, etc. The convolutional neural network (CNN) is an efficient approach to represent complex systems with large degrees of freedom. On the other hand, the generative adversarial network (GAN), as an unsupervised learning algorithm, is capable of efficiently imitating the distribution of training data. Here we leverage this unique property of GAN, in conjunction with CNN methodology, to establish an Ising simulator whose generator can produce Ising states given temperature T around the criticality. The generated Ising states well resemble, and essentially replicate, the data from conventional Monte Carlo simulations. Our results demonstrate the universality of GAN as a promising tool in the field of computational and statistical physics.