Can a CNN trained on the Ising model detect the phase transition of the <i>q</i>-state Potts model?
Kimihiko Fukushima, Kazumitsu Sakai
Abstract
Abstract Employing a deep convolutional neural network (deep CNN) trained on spin configurations of the 2D Ising model and the temperatures, we examine whether the deep CNN can detect the phase transition of the 2D $q$-state Potts model. To this end, we generate binarized images of spin configurations of the $q$-state Potts model ($q\ge 3$) by replacing the spin variables $\{0,1,\ldots,\lfloor q/2\rfloor-1\}$ and $\{\lfloor q/2\rfloor,\ldots,q-1\}$ with $\{0\}$ and $\{1\}$, respectively. Then, we input these images to the trained CNN to output the predicted temperatures. The binarized images of the $q$-state Potts model are entirely different from Ising spin configurations, particularly at the transition temperature. Moreover, our CNN model is not trained on the information about whether phases are ordered/disordered but is naively trained by Ising spin configurations labeled with temperatures at which they are generated. Nevertheless, the deep CNN can detect the transition point with high accuracy, regardless of the type of transition. We also find that, in the high-temperature region, the CNN outputs the temperature based on the internal energy, whereas, in the low-temperature region, the output depends on the magnetization and possibly the internal energy as well. However, in the vicinity of the transition point, the CNN may use more general factors to detect the transition point.