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Inverted Berezinskii-Kosterlitz-Thouless singularity and high-temperature algebraic order in an Ising model on a scale-free hierarchical-lattice small-world network
We have obtained exact results for the Ising model on a hierarchical lattice incorporating three key features characterizing many real-world networks---a scale-free degree distribution, a high clustering coefficient, and the small-world effect. By varying the probability $p$ of long-range bonds, the entire spectrum from an unclustered, non-small-world network to a …