Condensed Matter Physics, 2013, vol. 16, No. 2, 23001:1-12
On thermodynamic states of the Ising model on scale-free graphs
(Institute of Mathematics, Maria Curie-Sklodowska University, 20-031 Lublin, Poland)
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., S. N. Dorogovtsev et al, Rev. Mod. Phys., 80, 1275 (2008). 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.
random graphs, paramagnetic phase, percolation, branching process
05.70.Fh, 05.50.+q, 02.50.Ga