A universal neural network for learning phases and criticalities

TL;DR

This paper introduces a universal neural network trained on 1D data that can accurately determine critical points in various 3D models of phase transitions without retraining, demonstrating broad applicability and efficiency.

Contribution

A novel, highly universal neural network trained on 1D data that generalizes to multiple 3D models for identifying phase criticalities without additional training.

Findings

Successfully predicts critical points in 3D models using 1D training data.

No real configurations needed during testing, only bulk quantities or microscopic states.

Demonstrates broad applicability across different models with a single trained network.

Abstract

A universal supervised neural network (NN) relevant to compute the associated criticalities of real experiments studying phase transitions is constructed. The validity of the built NN is examined by applying it to calculate the criticalities of several three-dimensional (3D) models on the cubic lattice, including the classical $O(3)$ model, the 5-state ferromagnetic Potts model, and a dimerized quantum antiferromagnetic Heisenberg model. Particularly, although the considered NN is only trained one time on a one-dimensional (1D) lattice with 120 sites, yet it has successfully determined the related critical points of the studied 3D systems. Moreover, real configurations of states are not used in the testing stage. Instead, the employed configurations for the prediction are constructed on a 1D lattice of 120 sites and are based on the bulk quantities or the microscopic states of the considered models. As a result, our calculations are ultimately efficient in computation and the applications of the built NN is extremely broaden. 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 lead to a highly universal supervised neural network for learning phases and criticalities of 3D models. Based on the outcomes presented in this study, it is favorably probable that much simpler but yet elegant machine learning techniques can be constructed for fields of many-body systems other than the critical phenomena.