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

Takehisa Hasegawa, Koji Nemoto

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

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
Volume75
Issue number2
DOIs
Publication statusPublished - 2007 Feb 21

ASJC Scopus subject areas

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

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