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在统计物理模型中的碎形深度第一搜索路径.

Qiyuan Shi1, Youjin Deng1,2,3, Ming Li4

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深度首次搜索 (DFS) 路径在统计物理模型中揭示了碎形属性. 这种几何探测器提供了超越传统方法对关键现象的新见解.

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科学领域:

  • 统计物理 统计物理
  • 复杂的系统复杂的系统.
  • 几何探测器 几何探测器

背景情况:

  • 碎形属性对于理解关键现象至关重要.
  • 传统的可观测值可能无法完全捕捉复杂的系统行为.

研究的目的:

  • 为了研究深度首次搜索 (DFS) 路径的碎形特征.
  • 在统计物理模型的关键配置中探索DFS路径.
  • 评估DFS作为一种用于关键现象的新型几何探测器.

主要方法:

  • 在二维O (n) 循环模型中分析DFS路径和债券透.
  • 在各种维度 (d=2到6) 和关键系统中进行检查.
  • 计算DFS路径的碎形维度.

主要成果:

  • 在O (n) 循环模型中,DFS路径表现出一致的分形维度d_{DFS}=1+g/8.
  • 在跨维的债券透中观察到的DFS路径的非微不足道的分量缩放.
  • DFS 路径在 2D 格子中表现出碎形行为,并在更高的维度中填充空间.

结论:

  • 深度首次搜索 (DFS) 为关键现象提供了强大的几何探测器.
  • DFS路径分析提供了超出统计物理学的传统可观测值的洞察力.
  • DFS路径的碎形性质是复杂系统研究的一个重要发现.