Ferromagnetic Ising spin systems on the growing random tree

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 + alpha . 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 alpha as tanh(J/T(s)) = alpha/[2(alpha+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.