AI 中文总结
研究发现无标度网络自旋模型因度异质性产生类似维德曼线，用退火网络近似分析，如阿什金 - 泰勒和隐形Potts模型，该线在度指数有限范围存在，分隔不同有序状态并产生超临界态，为理解复杂网络集体动力学开辟新方向。
AI 中文摘要
维德曼线最初被确定为水和超临界流体中类似液体和类似气体行为之间的交叉线，分隔了这两种行为。本文表明，由于度的异质性，在无标度网络上的自旋模型中会出现类似的线，我们使用退火网络近似对其进行分析。对于阿什金 - 泰勒模型和隐形Potts模型，维德曼线存在于度指数的有限范围内。它分隔了两种不同的有序状态——分布式自旋排列和中心主导排列，同时还产生了一种超临界状状态，其中两种排列变得难以区分。这些结果表明，仅度的异质性就能产生超越传统相变理论的介观交叉，为理解和控制复杂网络中的集体动力学开辟了新方向。
英文摘要
The Widom line, initially identified as a crossover line between liquid-like and gas-like behavior in water and supercritical fluids, separates these two types of behavior. Here, we show that an analogous line arises in spin models on scale-free networks as a consequence of degree heterogeneity, which we analyze using the annealed network approximation. For the Ashkin--Teller and Invisible Potts models, the Widom line exists within a finite range of the degree exponent. It separates two distinct ordered regimes$-$distributed spin alignment and hub-dominant alignment$-$while also giving rise to a supercritical-like state where the two alignments become indistinguishable. These results demonstrate that degree heterogeneity alone can generate mesoscopic crossovers beyond conventional phase-transition theory, opening new directions for understanding and controlling collective dynamics in complex networks.
Comments26 pages, 11 figures
Journal refPhysical Review E 113.5 (2026): 055410
