Berezinskii-Kosterlitz-Thouless transition - A universal neural network study with benchmarks

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.

Automated summary

By using a supervised neural network trained on a one-dimensional lattice, the study successfully calculated the Berezinskii-Kosterlitz-Thouless phase transitions of two-dimensional classical XY models. The neural network approach proved to be accurate in predicting critical points with minimal information and demonstrated efficiency in computation. This universal neural network is not only valid for symmetry breaking related phase transitions, but also for calculating critical points associated with topology.