TY - JOUR

T1 - Susceptibility of the Ising model on the scale-free network with a Cayley tree-like structure

AU - Hasegawa, Takehisa

AU - Nemoto, Koji

N1 - Funding Information:
This work is supported by the 21st Century Center of Excellence (COE) program entitled “Topological Science and Technology”, Hokkaido University.

PY - 2008/2/15

Y1 - 2008/2/15

N2 - 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.

AB - 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.

KW - Cayley tree

KW - Ising model

KW - Magnetic susceptibility

KW - Networks

KW - Scale-free networks

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U2 - 10.1016/j.physa.2007.10.041

DO - 10.1016/j.physa.2007.10.041

M3 - Article

AN - SCOPUS:36748998966

VL - 387

SP - 1404

EP - 1410

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 5-6

ER -