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000894422 1001_ $$0P:(DE-Juel1)184900$$aMerger, Claudia Lioba$$b0$$eCorresponding author
000894422 245__ $$aGlobal hierarchy vs. local structure: Spurious self-feedback in scale-free networks
000894422 260__ $$aCollege Park, MD$$bAPS$$c2021
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000894422 500__ $$aThis work received further support by:  - JARA-HPC - the DFG through RTG 1995 -  RWTH Exploratory Research Space Seed Funds - JARA Center for Doctoral studies within the graduate School for Simulation and Data Science (SSD) - Excellence Strategy of the Federal Government and the Länder (G:(DE-82)EXS-PF-JARA-SDS005)
000894422 520__ $$aNetworks with fat-tailed degree distributions are omnipresent across many scientific disciplines. Such systems are characterized by so-called hubs, specific nodes with high numbers of connections to other nodes. By this property, they are expected to be key to the collective network behavior, e.g., in Ising models on such complex topologies. This applies in particular to the transition into a globally ordered network state, which thereby proceeds in a hierarchical fashion, and with a nontrivial local structure. Standard mean-field theory of Ising models on scale-free networks underrates the presence of the hubs, while nevertheless providing remarkably reliable estimates for the onset of global order. Here we expose that a spurious self-feedback effect, inherent to mean-field theory, underlies this apparent paradox. More specifically, we demonstrate that higher order interaction effects precisely cancel the self-feedback on the hubs, and we expose the importance of hubs for the distinct onset of local versus global order in the network. Due to the generic nature of our arguments, we expect the mechanism that we uncover for the archetypal case of Ising networks of the Barabási-Albert type to be also relevant for other systems with a strongly hierarchical underlying network structure.
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000894422 7001_ $$0P:(DE-HGF)0$$aReinartz, Timo$$b1
000894422 7001_ $$0P:(DE-HGF)0$$aWessel, Stefan$$b2
000894422 7001_ $$0P:(DE-HGF)0$$aHonerkamp, Carsten$$b3
000894422 7001_ $$0P:(DE-HGF)0$$aSchuppert, Andreas$$b4
000894422 7001_ $$0P:(DE-Juel1)144806$$aHelias, Moritz$$b5
000894422 773__ $$0PERI:(DE-600)3004165-X$$a10.1103/PhysRevResearch.3.033272$$gVol. 3, no. 3, p. 033272$$n3$$p033272$$tPhysical review research$$v3$$x2643-1564$$y2021
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