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

Takehisa Hasegawa; Koji Nemoto

doi:10.1016/j.physa.2007.10.041

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

Takehisa Hasegawa, Koji Nemoto

INF - Applied Information Sciences

Research output: Contribution to journal › Article › peer-review

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 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
Pages (from-to)	1404-1410
Number of pages	7
Journal	Physica A: Statistical Mechanics and its Applications
Volume	387
Issue number	5-6
DOIs	https://doi.org/10.1016/j.physa.2007.10.041
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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title = "Susceptibility of the Ising model on the scale-free network with a Cayley tree-like structure",

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.",

keywords = "Cayley tree, Ising model, Magnetic susceptibility, Networks, Scale-free networks",

author = "Takehisa Hasegawa and Koji Nemoto",

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

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

Abstract

Keywords

ASJC Scopus subject areas

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