Studies of the 2D Potts Model via Convolutional Neural Network

In this poster, employing a convolutional neural network (CNN), we investigate a new aspect of the phase transition for the 2D Potts models. First, we train the CNN by images of spin configurations labeled with their temperatures. Namely, the trained CNN can predict the temperature of the snapshot of an Ising spin configuration. Second, we examine whether the trained CNN by the Ising configuration can detect the phase transition of the 3- and 4-state Potts models. To this end, in the image of the Potts configurations, we divide the three (resp. four) types of spins 1,2,3 (resp. 1, 2, 3, 4) for the 3-state (resp. 4-state) Potts model into two parts, say {1,2} and 3 (resp. {1,2} and {3,4}), and then replace {1,2} with spin up and 3 (resp. {3,4}) with spin down. We call them the filtered Potts model. Of course, the geometric properties of the filtered Potts configuration at its critical point is completely different from the critical Ising configuration. Nevertheless, the CNN can recognize the phase transition of the filtered Potts model with high accuracy.