The fate of cities under natural hazards depends not only on hazard intensity but also on the coupling of structural damage, a collective process that remains poorly understood. Here we show that urban structural damage exhibits phase-transition phenomena. As hazard intensity increases, the system can shift abruptly from a largely safe to a largely damaged state, analogous to a first-order phase transition in statistical physics. Higher diversity in the building portfolio smooths this transition, but multiscale damage clustering traps the system in an extended critical-like regime (analogous to a Griffiths phase), suppressing the emergence of a more predictable disordered (Gaussian) phase. These phenomenological patterns are characterized by a random-field Ising model, with the external field, disorder strength, and temperature interpreted as the effective hazard demand, structural diversity, and modeling uncertainty, respectively. Applying this framework to real urban inventories reveals that widely used engineering modeling practices can shift urban damage patterns between synchronized and volatile regimes, systematically biasing exceedance-based risk metrics by up to 50% under moderate earthquakes ($M_w \approx 5.5$--$6.0$), equivalent to a several-fold gap in repair costs. This phase-aware description turns the collective behavior of civil infrastructure damage into actionable diagnostics for urban risk assessment and planning.

翻译：城市在自然灾害中的命运不仅取决于灾害强度，还取决于结构损伤的耦合效应——这一集体过程目前仍认知有限。本文揭示城市结构损伤具有相变现象：随灾害强度增加，系统可能从基本安全状态突变为严重受损状态，类似于统计物理学中的一级相变。建筑存量的多样性越高，该转变越平滑，但多尺度损伤集群效应会使系统陷入类似格里菲斯相的扩展临界态，抑制更可预测的无序（高斯）相出现。这些现象学模式可通过随机场伊辛模型表征，其中外场、无序强度与温度分别对应有效灾害需求、结构多样性及建模不确定性。将该框架应用于实际城市建筑清单发现，广泛采用的工程建模方法可使城市损伤模式在同步态与波动态之间切换，在中等地震（$M_w \approx 5.5$~$6.0$）条件下导致基于超阈值风险指标的系统性偏差高达50%，相当于维修成本数倍的差距。这种考虑相变的描述方式将民用基础设施损伤的集体行为转化为城市风险评估与规划的可操作诊断指标。