Title: Berezinskii--Kosterlitz--Thouless transition -- a universal neural network study with benchmarking Show Chinese title

Title: 贝雷津斯基-科尔斯特里茨-陶斯利相变——具有基准测试的通用神经网络研究

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. Show Chinese abstract

Abstract: 使用一次在二维晶格的200个位点上训练的监督神经网络（NN），我们计算了二维（2D）经典$XY$和二维广义经典$XY$模型的Berezinskii--Kosterlitz--Thouless相变。 特别是，体量的Binder比值和所研究系统的自旋状态被用来构建NN预测所需的配置。 通过将半经验有限尺寸标度应用于相关数据，NN方法得到的临界点与文献中建立的已知结果吻合良好。 这表明，对于每个考虑的模型，确定其各个相只需要少量信息。 这里呈现的结果明确表明，所使用的通用NN不仅适用于与对称性破缺相关的相变，而且也适用于计算与拓扑相关的相变的临界点。 通过进行若干详细的基准计算，检验了所用NN在计算中的效率。