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We analyze the ferromagnetic Ising model on a scale-free tree; the growingrandom network model with the linear attachment kernel $A_k=k+\alpha$introduced by [Krapivsky et al.: Phys. Rev. Lett. {\bf 85} (2000) 4629-4632].We derive an estimate of the divergent temperature $T_s$ below which thezero-field susceptibility of the system diverges. Our result shows that $T_s$is related to $\alpha$ as $\tanh(J/T_s)=\alpha/[2(\alpha+1)]$, where $J$ is theferromagnetic interaction. An analysis of exactly solvable limit for the modeland numerical calculation support the validity of this estimate.

Ferromagnetic Ising spin systems on the growing random tree