在Ising,Blume-Capel和Ising-metamagnet模型中对相变的机器学习研究
Vasanth Kumar Babu1, Rahul Pandit1
1Indian Institute of Science, Bangalore, Centre for Condensed Matter Theory, Department of Physics, 560012, India.
Physical review. E
|August 1, 2025
概括
这项研究将机器学习与模拟集成在一起,以分析旋转模型中的相位过渡. 它介绍了计算关键指数和缩放函数的新方法,推进了我们对磁系统的理解.
科学领域:
- 统计物理学的统计物理.
- 计算物理学的计算物理.
- 机器学习应用程序 机器学习应用程序
背景情况:
- 关于相位转换的传统研究往往侧重于特定的指数,如 ν.
- 精确确定关键指数 (y_t,y_h) 和缩放函数对于理解关键现象至关重要.
- 在不同类型的相变 (连续和第一阶段) 中研究普遍性和有限尺寸缩放 (FSS) 仍然是一个活跃的研究领域.
研究的目的:
- 开发和应用一种结合神经网络 (NN) 与蒙特卡洛 (MC) 模拟和有限尺寸缩放 (FSS) 的新型框架.
- 将分析扩展到相关度长指数 (ν) 以外,包括在临界点和三临界点上的热磁指数 (y_t, y_h).
- 研究这种综合方法对不同的旋转模型和过渡类型 (包括第一阶过渡) 的适用性.
主要方法:
- 使用神经网络 (NN) 来训练的数据从MC模拟的Ising型自旋模型在有限的网格.
- 应用有限尺寸缩放 (FSS) 技术与NN结合,以提取关键指数.
- 开发用于连续和第一阶段过渡的FSS的方法,以及作为温度和磁场函数的NN输出.
主要成果:
- 成功结合了NN,MC模拟和FSS来确定临界点和三临界点的热磁指数 (y_t,y_h).
- 在Ising类型的临界点展示了NN对应的双尺度因子普遍性.
- 已建立的FSS用于第一阶段的转换和衍生FSS形式用于训练的NN输出.
结论:
- 机器学习与传统的模拟和缩放技术的整合为研究阶段过渡提供了一种强大的新方法.
- 这种方法推进了关键指数和缩放函数的计算,为磁自旋系统的行为提供了更深入的见解.
- 该框架具有多功能性,适用于各种旋转模型和过渡类型,为未来计算统计物理学研究铺平了道路.
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