标题： 尺度不变网络中的几何临界性 显示英文标题

标题： Geometric Criticality in Scale-Invariant Networks

摘要： 物理系统中的维度决定了临界状态下的普遍性质。 然而，结构扰动对维度的影响仍大多未被探索。 在这里，我们从重整化群的角度表征了尺度不变网络中结构固定点的吸引域，证明了吸引域稳定性与结构相变有关。 这种拓扑依赖效应，我们称之为几何临界性，触发了一种此前未知的几何破坏，这导致了非平凡的分形维度，并揭示了通向不稳定结构固定点的隐藏流。 我们对网络和格子如何响应无序的系统研究，为未来分析由冻结无序引起的非遍历行为奠定了基础。 显示英文摘要

摘要： Dimension in physical systems determines universal properties at criticality. Yet, the impact of structural perturbations on dimensionality remains largely unexplored. Here, we characterize the attraction basins of structural fixed points in scale-invariant networks from a renormalization group perspective, demonstrating that basin stability connects to a structural phase transition. This topology-dependent effect, which we term geometric criticality, triggers a geometric breakdown hereto unknown, which induces non-trivial fractal dimensions and unveils hidden flows toward unstable structural fixed points. Our systematic study of how networks and lattices respond to disorder paves the way for future analysis of non-ergodic behavior induced by quenched disorder.