Correlations in interacting systems with a network topology
Correlations in interacting systems with a network topology
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DOI：
10.1103/physreve.72.066130
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发表时间：
2005-12-01
影响因子：
2.4
通讯作者：
Mendes, JFF
中科院分区：
文献类型：
--
作者：
Dorogovtsev, SN;Goltsev, AV;Mendes, JFF
我们研究放置在复杂网络上的相互作用系统中的对相关性。我们表明，通常在这些系统中，相互作用的对象（例如，自旋）的平均衰减速度快于1/（lz（π））。这里z（l）是网络中顶点的第l个最近邻居的平均数。特别是，这种行为会导致具有厚尾度分布的网络中第二个和更远的邻居之间的相关性急剧减弱，在无限网络极限中，这些网络具有发散数z（2）。在这类大型网络中，只有最近的邻居之间的配对相关性才是真正可观察的。我们找到了一个复杂网络上的伊辛模型的对相关函数。这个确切的结果是由现象学的方法证实。
We study pair correlations in interacting systems placed on complex networks. We show that usually in these systems, pair correlations between interacting objects (e.g., spins), separated by a distance l, decay, on average, faster than 1/(lz(epsilon)). Here z(l) is the mean number of the lth nearest neighbors of a vertex in a network. This behavior, in particular, leads to a dramatic weakening of correlations between second and more distant neighbors on networks with fat-tailed degree distributions, which have a divergent number z(2) in the infinite network limit. In large networks of this kind, only pair correlations between the nearest neighbors are actually observable. We find the pair correlation function of the Ising model on a complex network. This exact result is confirmed by a phenomenological approach.