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

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) alpha k(-gamma) 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 gamma > 3, while it diverges at any finite temperature for gamma <= 3, and (ii) the surface part diverges below the divergence temperature of the SF network with the Cayley tree-like structure T-s for gamma > 3, while it diverges at any finite temperature for y <= 3. (c) 2007 Elsevier B.V. All rights reserved.