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Correlations in interacting systems with a network topology | | S.N. Dorogovtsev
; A.V. Goltsev
; J.F.F. Mendes
; | | Date: |
31 May 2005 | | Subject: | Statistical Mechanics; Physics and Society; Networking and Internet Architecture; Mathematical Physics | cond-mat.stat-mech cs.NI math-ph math.MP physics.soc-ph | | Abstract: | We study pair correlations in cooperative systems placed on complex networks. We show that usually in these systems, the correlations between two interacting objects (e.g., spins), separated by a distance $ell$, decay, on average, faster than $1/(ell z_ell)$. Here $z_ell$ is the mean number of the $ell$-th 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 this case, only the pair correlations between the nearest neighbors are observable. We obtain the pair correlation function of the Ising model on a complex network and also derive our results in the framework of a phenomenological approach. | | Source: | arXiv, cond-mat/0506002 | | Services: | Forum | Review | PDF | Favorites | |
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