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

Takehisa Hasegawa, Koji Nemoto

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

We derive the exact expression for the zero-field susceptibility of each spin of the Ising model on the scale-free (SF) network having the degree distribution P (k) ∝ k- γ with the Cayley tree-like structure. The system shows that: (i) the zero-field susceptibility of a spin in the interior part diverges below the transition temperature of the SF network with the Bethe lattice-like structure Tc for γ > 3, while it diverges at any finite temperature for γ ≤ 3, and (ii) the surface part diverges below the divergence temperature of the SF network with the Cayley tree-like structure Ts for γ > 3, while it diverges at any finite temperature for γ ≤ 3.

Original languageEnglish
Pages (from-to)1404-1410
Number of pages7
JournalPhysica A: Statistical Mechanics and its Applications
Volume387
Issue number5-6
DOIs
Publication statusPublished - 2008 Feb 15

Keywords

  • Cayley tree
  • Ising model
  • Magnetic susceptibility
  • Networks
  • Scale-free networks

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics

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