### 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 T_{c} 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 T_{s} for γ > 3, while it diverges at any finite temperature for γ ≤ 3.

Original language | English |
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Pages (from-to) | 1404-1410 |

Number of pages | 7 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 387 |

Issue number | 5-6 |

DOIs | |

Publication status | Published - 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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## Cite this

Hasegawa, T., & Nemoto, K. (2008). Susceptibility of the Ising model on the scale-free network with a Cayley tree-like structure.

*Physica A: Statistical Mechanics and its Applications*,*387*(5-6), 1404-1410. https://doi.org/10.1016/j.physa.2007.10.041