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@ARTICLE{Merger:894422,
      author       = {Merger, Claudia Lioba and Reinartz, Timo and Wessel, Stefan
                      and Honerkamp, Carsten and Schuppert, Andreas and Helias,
                      Moritz},
      title        = {{G}lobal hierarchy vs. local structure: {S}purious
                      self-feedback in scale-free networks},
      journal      = {Physical review research},
      volume       = {3},
      number       = {3},
      issn         = {2643-1564},
      address      = {College Park, MD},
      publisher    = {APS},
      reportid     = {FZJ-2021-03215},
      pages        = {033272},
      year         = {2021},
      note         = {This 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)},
      abstract     = {Networks 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.},
      cin          = {INM-6 / IAS-6 / INM-10},
      ddc          = {530},
      cid          = {I:(DE-Juel1)INM-6-20090406 / I:(DE-Juel1)IAS-6-20130828 /
                      I:(DE-Juel1)INM-10-20170113},
      pnm          = {5232 - Computational Principles (POF4-523)},
      pid          = {G:(DE-HGF)POF4-5232},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000705662100002},
      doi          = {10.1103/PhysRevResearch.3.033272},
      url          = {https://juser.fz-juelich.de/record/894422},
}