论文标题
berezinskii-kosterlitz-从神经网络流过的无与伦比的过渡
Berezinskii-Kosterlitz-Thouless transition from Neural Network Flows
论文作者
论文摘要
我们采用神经网络流（NN流）方法来研究Berezinskii-Kosterlitz-thouless-thouless（BKT）相变的2维Q-State时钟模型，并使用$ Q \ ge 4 $。 NN流程由相同单元的序列组成，以进行流动。该单元是一种由蒙特卡洛配置的数据训练，以无监督的学习方式训练。为了衡量在不同温度下蒙特卡洛构型的差异以及NN-流动状态合奏的独特性，我们采用Jesen-Shannon Divergence（JSD）作为信息距离措施“温度计”。该JSD温度计比较了两个状态集合的平均磁化的概率分布函数。我们的结果表明，NN流将在固定点整体中以任意旋转状态流到某些状态。定点集合的相应JSD采用具有特殊特征的唯一配置文件，这可以帮助识别基础蒙特卡洛构型的BKT相变的临界温度。
We adopt the neural network flow (NN flow) method to study the Berezinskii-Kosterlitz-Thouless (BKT) phase transitions of the 2-dimensional q-state clock model with $q\ge 4$. The NN flow consists of a sequence of the same units to proceed the flow. This unit is a variational autoencoder (VAE) trained by the data of Monte-Carlo configurations in the way of unsupervised learning. To gauge the difference among the ensembles of Monte-Carlo configurations at different temperatures and the uniqueness of the ensemble of NN-flowed states, we adopt the Jesen-Shannon divergence (JSD) as the information-distance measure "thermometer". This JSD thermometer compares the probability distribution functions of the mean magnetization of two ensembles of states. Our results show that the NN flow will flow an arbitrary spin state to some state in a fixed-point ensemble of states. The corresponding JSD of the fixed-point ensemble takes a unique profile with peculiar features, which can help to identify the critical temperatures of BKT phase transitions of the underlying Monte-Carlo configurations.
