不通过随机步行访问的网站的相关透的临界指数
Raz Halifa Levi1, Yacov Kantor2
1The Faculty of Engineering, <a href="https://ror.org/04mhzgx49">Tel Aviv University</a>, Tel Aviv 6997801, Israel.
Physical review. E
|September 19, 2024
概括
我们使用3-5维度的随机步行来研究现场透. 大到第二大集群的比例有助于找到关键点,指数β和γ描述集群属性.
科学领域:
- 统计物理 统计物理
- 透理论 透理论
- 随机步行 随机步行
背景情况:
- 透理论研究了随机系统中的连接性.
- 随机走在格子上是统计力学中的基础.
- 相关透引入了标准模型中不存在的依赖关系.
研究的目的:
- 调查一个d维相关的透问题.
- 通过随机步行分析未被访问的网站形成的集群的属性.
- 确定控制临界点附近几何属性的临界指数.
主要方法:
- 在超立方格上模拟了一条长度为N=uL^d的随机步行,L^d为d=3,4,5.
- 利用平均最大集群质量 (M1) 与第二大集群质量 (M2) 的比率来确定临界值 (uc).
- 使用有限尺寸缩放计算了关键指数β (跨集群强度) 和γ (平均有限集群大小S).
主要成果:
- 在 uc 处的 M1/M2 比率证明独立于格子大小 L,作为 uc 的可靠指标.
- 在所有研究的维度中,指数β始终接近1.
- 指数γ表现出一个下降的趋势与不断增加的维度 (≈3.9在d=3,≈1.9在d=4,≈1.3在d=5),接近1在d=6.的理论值.
结论:
- M1/M2比提供了一个可靠的方法来确定这个相关的透模型中的关键点.
- 计算的临界指数β和γ为集群属性的维度依赖提供了宝贵的见解.
- 结果与理论预测一致,特别是随着维度的增加,g的趋势向1的趋势.
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