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arXiv · 1109.4546

On thermodynamic states of the Ising model on scale-free graphs

Yuri Kozitsky
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Abstract

There is proposed a model of scale-free random graphs which are locally close to the uncorrelated complex random networks with divergent $\langle k^2 \rangle$ studied in e.g. S. N. Dorogovtsev {\it et al}, Rev. Mod. Phys. {\bf 80}, 1275 (2008). It is shown that the Ising model on these 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. Possible extensions are discussed.

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Yuri Kozitsky. 2011-09-21. On thermodynamic states of the Ising model on scale-free graphs. https://arxiv.org/abs/1109.4546

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