A universal neural network for learning phases

A universal supervised neural network (NN) relevant to compute the associated critical points of real experiments studying phase transitions is constructed. The validity of the built NN is examined by applying it to calculate the critical points of several three-dimensional (3D) and two-dimensional (2D) models, including the 3D classical O(3) model, the 3D 5-state ferromagnetic Potts model, a 3D dimerized quantum antiferromagnetic Heisenberg model, and the 2D XY model. Particularly, although the considered NN is only trained once on a one-dimensional (1D) lattice with 120 sites, it has successfully determined the related critical points of the studied systems. Moreover, real configurations of states are not used in the testing stage. Instead, the employed configurations for the NN prediction are constructed on a 1D lattice of 120 sites and are based on the bulk quantities or the spin states of the considered models. As a result, our calculations are ultimately efficient in computation, and the application of the built NN in studying the phase transitions of physical systems is extremely broad. Considering the fact that the investigated systems vary dramatically from each other, it is amazing that the combination of these two strategies in the training and the testing stages leads to a highly universal supervised neural network for learning phases of 3D and 2D models. Based on the outcomes presented in this study, it is favorably probable that much simpler but elegant machine learning techniques can be constructed for fields of many-body systems other than the critical phenomena.