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 -