Abstract
There is proposed a model of scale-free random graphs which are locally close to the uncorrelated complex random networks with divergent 〈k2〉 studied in, e.g., Dorogovtsev S.N. et al., Rev. Mod. Phys., 2008, 80, 1275. It is shown that the Ising model on the proposed graphs with interaction intensities of arbitrary signs with probability one is in a paramagnetic state at sufficiently high finite values of the temperature. For the same graphs, the bond percolation model with probability one is in a nonpercolative state for positive values of the percolation probability. These results and their possible extensions are also discussed.
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