Ferromagnetic Ising spin systems on the growing random tree

We analyze the ferromagnetic Ising model on a scale-free tree; the growing random tree model with the linear attachment kernel Ak =k+α. We derive an estimate of the divergent temperature Ts below which the zero-field susceptibility of the system diverges. Our result shows that Ts is related to α as tanh (J/ Ts) =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.