This paper presents a systematic study of the application of convolutional neural networks (CNNs) as an efficient and versatile tool for the analysis of critical and low-temperature phase states in spin system models. The problem of calculating the dependence of the average energy on the spatial distribution of exchange integrals for the Edwards-Anderson model on a square lattice with frustrated interactions is considered. We further construct a single convolutional classifier of phase states of the ferromagnetic Ising model on square, triangular, honeycomb, and kagome lattices, trained on configurations generated by the Swendsen-Wang cluster algorithm. Computed temperature profiles of the averaged posterior probability of the high-temperature phase form clear S-shaped curves that intersect in the vicinity of the theoretical critical temperatures and allow one to determine the critical temperature for the kagome lattice without additional retraining. It is shown that convolutional models substantially reduce the root-mean-square error (RMSE) compared with fully connected architectures and efficiently capture complex correlations between thermodynamic characteristics and the structure of magnetic correlated systems.

翻译：本文系统研究了卷积神经网络（CNNs）作为一种高效且通用的工具，在自旋系统模型中用于分析临界态和低温相态的应用。针对具有阻挫相互作用的方形晶格上的Edwards-Anderson模型，探讨了计算平均能量对交换积分空间分布依赖性的问题。我们进一步构建了一个单一卷积分类器，用于识别方形、三角形、蜂窝和kagome晶格上铁磁Ising模型的相态，该分类器基于Swendsen-Wang团簇算法生成的构型进行训练。计算得到的高温相平均后验概率的温度剖面形成清晰的S形曲线，这些曲线在理论临界温度附近相交，从而无需额外再训练即可确定kagome晶格的临界温度。研究表明，与全连接架构相比，卷积模型显著降低了均方根误差（RMSE），并有效捕捉了热力学特性与磁性关联系统结构之间的复杂相关性。