经典XY模型的临界温度通过自编码器隐性空间采样
Brandon Willnecker1, Mervlyn Moodley1
1University of KwaZulu-Natal, School of Chemistry and Physics, Westville Campus, Private Bag X54001, Durban, 4000, South Africa.
Physical review. E
|February 20, 2025
概括
研究人员开发了一种机器学习方法来检测XY模型中的Berezinskii-Kosterlitz-Thouless (BKT) 过渡. 这种方法使用自编码器来分析密度,成功地确定了这个拓相位过渡的临界温度.
科学领域:
- 凝聚物质物理学 凝聚物质物理学
- 统计力学 统计力学
- 机器学习应用 机器学习应用
背景情况:
- 经典的XY模型是统计力学的一个基本系统.
- 两个维的XY模型表现出一种被称为Berezinskii-Kosterlitz-Thouless (BKT) 过渡的拓相过渡.
- 了解BKT过渡对于描述物理系统中的拓现象至关重要.
研究的目的:
- 提出一种基于机器学习的新方法来识别BKT的阶段过渡.
- 克服与U(1) 对称性相关的挑战,以生成用于分析的独特状态.
- 准确确定BKT过渡的临界温度.
主要方法:
- 引入一个辅助场来表示旋密度并减轻U(1) 对称性.
- 使用自动编码器将辅助场映射到一个低维的潜空间.
- 从潜空间取样,以计算密度的热平均值.
主要成果:
- 机器学习方法成功地确定了BKT阶段过渡的出现.
- 密度的热平均值使用潜空间的样本准确计算.
- 用拟议的方法确定了相变的临界温度.
结论:
- 机器学习为分析物理模型中的拓相变提供了一个强大的工具.
- 开发的辅助场和自动编码器方法有效地处理对称性问题.
- 这种方法提供了一种可靠的方式来确定像XY模型这样的系统中的临界温度.
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