Machine learning phases and criticalities without using real data for training

TL;DR

This paper demonstrates that neural networks can accurately identify phase transitions in various physical models without using real or theoretical data for training, relying instead on unconventional training sets and finite-size scaling.

Contribution

Introduces a novel neural network training approach that does not require real or theoretical configurations, yet accurately detects critical points in diverse physical systems.

Findings

Neural networks accurately identify phase transition points.

Unconventional training sets are cost-effective and versatile.

Method aligns well with established literature results.

Abstract

We study the phase transitions of three-dimensional (3D) classical O(3) model and the two-dimensional (2D) classical XY model, as well as both the quantum phase transitions of 2D and 3D dimerized spin-1/2 antiferromagnets, using the techniques of supervised neural network (NN). Moreover, unlike the conventional approaches commonly used in the literature, the training sets employed in our investigation are neither the theoretical nor the real configurations of the considered systems. Remarkably, with such an unconventional set up of the training stage in conjunction with semi-experimental finite-size scaling formulas, the associated critical points determined by the NN method agree well with the established results in the literature. The outcomes obtained here imply that certain unconventional training strategies, like the one used in this study, are not only cost-effective in computation, but are also applicable for a wild range of physical systems.