拓科尔摩戈罗夫复杂性和贝雷津斯基-科斯特利茨-托勒斯机制
Vittorio Vitale1,2,3, Tiago Mendes-Santos4, Alex Rodriguez1,5
1International Centre for Theoretical Physics (ICTP), Strada Costiera 11, 34151 Trieste, Italy.
Physical review. E
|April 18, 2024
概括
在古典统计力学中,拓和复杂性是交织在一起的. 分区函数的科尔莫戈罗夫复杂性揭示了拓特征,特别是在跨越贝雷津斯基-科斯特利茨-托勒斯过渡的XY模型中.
科学领域:
- 统计力学 统计力学
- 复杂的系统复杂的系统.
- 拓物理 拓物理
背景情况:
- 拓在多体物理学中至关重要,它影响了从经典流到量子物质激发的现象.
- 拓效应与由非局部自由度控制的信息内容相关联.
- 拓学与多体状态 (分区函数) 的复杂性之间的确切关系尚不清楚.
研究的目的:
- 在古典统计力学中,建立拓与复杂性之间的直接联系.
- 开发一个理论,证明科尔摩戈罗夫复杂性如何量化分区函数采样中的拓特征.
- 调查拓刺激在系统复杂性中的作用.
主要方法:
- 开发了一种理论,将科尔摩戈罗夫复杂性与古典统计力学中的拓刺激联系起来.
- 在各种拓上分析了二维的伊辛,海森伯格和XY模型.
- 使用内在维度量化模型采样 (配置空间多元组) 的复杂性.
主要成果:
- 对于伊辛和海森伯格模型,内在维度是独立于拓的.
- 对于 XY 模型,在 Berezinskii-Kosterlitz-Thouless (BKT) 过渡温度下,内在维度变得取决于拓.
- 在BKT阶段,复杂性与多重同质性相关,对于g-torii,与属性相关.
结论:
- 多体系统中的拓现象可以通过科尔摩戈罗夫复杂性的透视来理解.
- 这项研究揭示了数据复杂性,拓和相位过渡之间的新联系.
- 条件连接成为关键的数据空间顺序参数,与拓复杂性相关.
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