Ising model on the scale-free network with a Cayley-tree-like structure

Takehisa Hasegawa, Koji Nemoto

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


We derive an exact expression for the magnetization and the zero-field susceptibility of the Ising model on a random graph with degree distribution P (k) ∝ k-γ and with a boundary consisting of leaves, that is, vertices whose degree is 1. The system has no magnetization at any finite temperature, and the susceptibility diverges below a certain temperature Ts depending on the exponent γ. In particular, Ts reaches infinity for γ≤4. These results are completely different from those of the case having no boundary, indicating the nontrivial roles of the leaves in the networks.

Original languageEnglish
Article number026105
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number2
Publication statusPublished - 2007 Feb 21
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


Dive into the research topics of 'Ising model on the scale-free network with a Cayley-tree-like structure'. Together they form a unique fingerprint.

Cite this