AI 中文总结
该研究构建非阿贝尔结构一致性理论，通过平行 tempering 模拟揭示 SU(2) 模型高无序相的非玻璃态关联规范液体特性，未发现热力学副本对称性破缺证据。
AI 中文摘要
我们为动力学变换位于单纯形网络链上的系统构建了结构一致性的非阿贝尔理论。规范协变性源于选择局部表示框架的自由度，而 plaquette 完整子（plaquette holonomies）量化了不同路径的不相容性。对于具有淬火随机 plaquette 耦合的完全单纯形 2-复形上的 SU(2) 模型，平行 tempering 模拟揭示了由无序驱动的全局相容性的连续损失。在高无序相中，均匀相容性 $M_P$ 随系统尺寸减小，积分相邻相关权重 $\bar{\tau}_{\text{adj}}$ 保持有限值。此外，连通副本重叠宽度趋近数值噪声底，且其分布变窄，未提供热力学副本对称性破缺的证据。因此，致密阻挫产生了一种非玻璃态的关联规范液体，其中单个对关联被几何稀释，同时有限的积分关联权重得以保留。
英文摘要
We formulate a non-Abelian theory of network compatibility in which dynamical transformations reside on the links. Gauge covariance follows from the freedom to choose local representation frames, while plaquette holonomies quantify the incompatibility of closed-loop transformations. For an SU(2) model on the complete simplicial 2-complex with quenched random plaquette couplings, parallel-tempering simulations reveal a continuous disorder-driven phase transition characterized by the network compatibility $M_P$. As the disorder strength approaches the critical value, the compatibility drops rapidly to a value that decreases with system size, while the frustration energy of the network sharply rises. Moreover, analysis of connected replica-overlap width provides no evidence for thermodynamic replica-symmetry breaking. Instead, the high-disorder regime sustains a nearly constant integrated adjacent correlation as the system size increases. Therefore, rather than a frozen gauge glass or a featureless disordered ``gas'' phase, dense topological frustration produces a non-glassy correlated gauge liquid in which individual pair correlations are geometrically diluted while a finite integrated correlation survives.
Comments4 pages, 2 figures. Feedback welcome! Modification in v2: supplemental material incoporated to main file, language modified, title changed, minor errors corrected, and previous figure presentation issue resolved
