Ostilli M, Ferreira A L, Mendes J F F
Departamento de Física and I3N, Universidade de Aveiro, Aveiro, Portugal.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jun;83(6 Pt 1):061149. doi: 10.1103/PhysRevE.83.061149. Epub 2011 Jun 28.
We analyze critical phenomena on networks generated as the union of hidden variable models (networks with any desired degree sequence) with arbitrary graphs. The resulting networks are general small worlds similar to those à la Watts and Strogatz, but with a heterogeneous degree distribution. We prove that the critical behavior (thermal or percolative) remains completely unchanged by the presence of finite loops (or finite clustering). Then, we show that, in large but finite networks, correlations of two given spins may be strong, i.e., approximately power-law-like, at any temperature. Quite interestingly, if γ is the exponent for the power-law distribution of the vertex degree, for γ≤3 and with or without short-range couplings, such strong correlations persist even in the thermodynamic limit, contradicting the common opinion that, in mean-field models, correlations always disappear in this limit. Finally, we provide the optimal choice of rewiring under which percolation phenomena in the rewired network are best performed, a natural criterion to reach best communication features, at least in noncongested regimes.
我们分析了由隐藏变量模型（具有任意期望度序列的网络）与任意图的并集生成的网络上的临界现象。由此产生的网络是类似于瓦茨和斯特罗加茨模型的一般小世界网络，但具有异质度分布。我们证明，有限环（或有限聚类）的存在不会改变临界行为（热临界或渗流临界）。然后，我们表明，在大型但有限的网络中，在任何温度下，两个给定自旋的相关性可能很强，即近似幂律形式。非常有趣的是，如果γ是顶点度的幂律分布的指数，对于γ≤3且有无短程耦合的情况，即使在热力学极限下，这种强相关性仍然存在，这与平均场模型中相关性在该极限下总是消失的普遍观点相矛盾。最后，我们给出了重连的最优选择，在这种选择下，重连网络中的渗流现象表现最佳，这是至少在非拥塞状态下实现最佳通信特性的自然标准。
