Correlations in interacting systems with a network topology
<|reference_start|>Correlations in interacting systems with a network topology: 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.<|reference_end|>
@article{dorogovtsev2005correlations,
    title={Correlations in interacting systems with a network topology},
    author={S.N. Dorogovtsev, A.V. Goltsev, J.F.F. Mendes},
    journal={Phys. Rev. E 72, 066130 (2005)},
    year={2005},
    doi={10.1103/PhysRevE.72.066130},
    archivePrefix={arXiv},
    eprint={cond-mat/0506002},
    primaryClass={cond-mat.stat-mech cs.NI math-ph math.MP physics.soc-ph}
}