用地面态训练的自动编码器检测三维伊辛模型相变
Detecting the 3D Ising model phase transition with a ground-state-trained autoencoder
AI总结：
本文提出一种单类深度学习框架，通过训练地面态配置的3D卷积神经网络自动编码器，检测三维伊辛模型的相变并恢复临界行为，得出临界温度和关联长度临界指数。
摘要：
我们开发了一种单类深度学习框架，用于检测相变并恢复三维伊辛模型的临界行为。一个仅在地面态配置上训练的3D卷积神经网络自动编码器（CAE）被开发出来，无需事先了解临界温度、哈密顿量或序参量。训练后，该模型应用于不同温度范围和不同晶格尺寸的蒙特卡罗配置。均方重建误差被证明对相变敏感。重建误差的有限尺寸标度分析得出临界温度T_c=4.5128(58)和关联长度临界指数ν=0.63(27)，与文献结果一致。我们的结果表明，仅在零温度配置上训练的单类CAE可以恢复三维伊辛模型的非平凡临界行为。
英文摘要：
We develop a one-class, deep-learning framework to detect the phase transition and recover critical behavior of the 3D Ising model. A 3D convolutional neural network autoencoder (CAE) is trained on ground-state configurations only, without prior knowledge of the critical temperature, the Hamiltonian, or the order parameter. After training, the model is applied to Monte Carlo configurations across a wide temperature range and different lattice sizes. The mean-square reconstruction error is shown to be sensitive to the transition. Finite-size scaling of the peak location for the reconstruction error susceptibility yields the critical temperature $T_c=4.5128(58)$ and the correlation-length critical exponent $ν=0.63(27)$, consistent with results from the literature. Our results show that a one-class CAE, trained on zero-temperature configurations only, can recover nontrivial critical behavior of the 3D Ising model.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
