An anomalous mean-field solution is known to capture the non trivial phase diagram of the Ising model in annealed complex networks. Nevertheless the critical fluctuations in random complex networks remain mean-field. Here we show that a break-down of this scenario can be obtained when complex networks are embedded in geometrical spaces. Through the analysis of the Ising model on annealed spatial networks, we reveal in particular the spectral properties of networks responsible for critical fluctuations and we generalize the Ginsburg criterion to complex topologies.
anomalous mean-field solution, complex networks, Ginsburg criterion
Statistical mechanics, Mean field theory, Ising model
Bradde, Serena; Caccioli, Fabio; Dall'Asta, Luca; and Bianconi, Ginestra, "Critical fluctuations in spatial complex networks" (2009). Physics Faculty Publications. Paper 90. http://hdl.handle.net/2047/d20000443
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