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作用——这一集体过程目前仍缺乏深入理解。本文揭示城市结构损伤呈现相变现象。随着灾害强度增加，系统可能从基本安全状态突然转变为大规模损伤状态，类似于统计物理学中的一级相变。建筑组合的更高多样性会平滑这一转变，但多尺度损伤聚类会将系统困于扩展的类临界状态（类似于格里菲斯相），抑制更可预测的无序（高斯）相的出现。这些唯象模式可通过随机场伊辛模型进行表征，其中外场、无序强度和温度分别解释为有效灾害需求、结构多样性和建模不确定性。将该框架应用于实际城市资产清单发现，广泛使用的工程建模实践可使城市损伤模式在同步状态与波动状态之间转换，在中等强度地震（$M_w \approx 5.5$--$6.0$）下，基于超越概率的风险指标会产生高达50%的系统性偏差，相当于修复成本出现数倍差异。这种基于相变的描述将土木基础设施损伤的集体行为转化为可用于城市风险评估与规划的可操作诊断工具。