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 language | English |
|---|---|
| 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