Berezinskii--Kosterlitz--Thouless transition -- a universal neural network study with benchmarking

TL;DR

This study demonstrates that a single trained neural network can accurately identify phase transitions, including topological ones, in 2D classical XY models using minimal data, validated through benchmarking.

Contribution

A universal neural network trained on 1D data effectively predicts phase transitions in 2D models, including topological transitions, with minimal additional training.

Findings

Neural network accurately predicts critical points in 2D XY models.

The approach works for both symmetry-breaking and topological phase transitions.

Benchmark tests confirm the efficiency and validity of the neural network method.

Abstract

Using a supervised neural network (NN) trained once on a one-dimensional lattice of 200 sites, we calculate the Berezinskii--Kosterlitz--Thouless phase transitions of the two-dimensional (2D) classical $XY$ and the 2D generalized classical $XY$ models. In particular, both the bulk quantities Binder ratios and the spin states of the studied systems are employed to construct the needed configurations for the NN prediction. By applying semiempirical finite-size scaling to the relevant data, the critical points obtained by the NN approach agree well with the known results established in the literature. This implies that for each of the considered models, the determination of its various phases requires only a little information. The outcomes presented here demonstrate convincingly that the employed universal NN is not only valid for the symmetry breaking related phase transitions, but also works for calculating the critical points of the phase transitions associated with topology. The efficiency of the used NN in the computation is examined by carrying out several detailed benchmark calculations.