English

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

Mathematical Physics 2011-09-22 v1 math.MP

Abstract

There is proposed a model of scale-free random graphs which are locally close to the uncorrelated complex random networks with divergent k2\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.

Keywords

Cite

@article{arxiv.1109.4546,
  title  = {On thermodynamic states of the Ising model on scale-free graphs},
  author = {Yuri Kozitsky},
  journal= {arXiv preprint arXiv:1109.4546},
  year   = {2011}
}