来自自动回归神经网络的自旋系统的相互信息
Piotr Białas1, Piotr Korcyl2, Tomasz Stebel2
1Institute of Applied Computer Science, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków, Poland.
Physical review. E
|November 18, 2023
概括
我们开发了一种新的蒙特卡洛方法,使用神经网络来计算自旋系统中的相互信息. 这种方法准确地研究了复杂系统的几何形状,并证实了远离临界温度的伊辛格模型的面积定律.
科学领域:
- 统计力学 统计力学
- 机器学习 机器学习
- 量子信息理论 量子信息理论
背景情况:
- 在复杂系统中估计相互信息是计算上具有挑战性的.
- 了解子系统属性对于凝聚物质物理学至关重要.
- 经典的旋转系统为理论方法提供了测试平台.
研究的目的:
- 引入一种直接和有效的方法来计算双边相互信息.
- 为了使古典旋转系统中任意子系统几何学的研究.
- 为应用在经典领域理论中的方法进行概括.
主要方法:
- 使用蒙特卡洛采样.
- 通过自回归神经网络提高采样效率.
- 将该方法应用于具有各种分区的伊辛模型.
主要成果:
- 该方法成功地估计了任意几何形状的双边相互信息.
- 在远离临界点的温度下,对伊辛格模型来说,面积定律得到了满足.
- 对于面积定律,观察到一个通用常数和一个取决于分区的系数.
结论:
- 提出的方法为分析复杂系统中的纠和相关性提供了一个强大的工具.
- 这些发现有助于理解统计力学中的关键现象和普遍性.
- 该技术的概括性为研究量子场理论开辟了道路.
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