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Ferromagnetic Ising spin systems on the growing random tree

Takehisa Hasegawa^*,† and Koji Nemoto

Department of Physics, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Sapporo, Hokkaido 060-0810, Japan

^*Present address: Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan.
^†hase@statphys.sci.hokudai.ac.jp

Phys. Rev. E 80, 026126 – Published 26 August, 2009

DOI: https://doi.org/10.1103/PhysRevE.80.026126

Abstract

We analyze the ferromagnetic Ising model on a scale-free tree; the growing random tree model with the linear attachment kernel $A_{k} = k + α$ . We derive an estimate of the divergent temperature $T_{s}$ below which the zero-field susceptibility of the system diverges. Our result shows that $T_{s}$ is related to $α$ as $tanh (J / T_{s}) = α / [2 (α + 1)]$ , where $J$ is the ferromagnetic interaction. An analysis of exactly solvable limit for the model and numerical calculation supports the validity of this estimate.

Article Text

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