  We study the critical behavior of the Ising model in annealed scale-free (SF)
networks of finite system size with forced upper cutoff in degree. By mapping
the model onto the weighted fully connected Ising model, we derive analytic
results for the finite-size scaling (FSS) near the phase transition,
characterized by the cutoff-dependent two-parameter scaling with four distinct
scaling regimes, in highly heterogeneous networks. These results are
essentially the same as those found for the nonequilibrium contact process in
annealed SF networks, except for an additional complication due to the trivial
critical point shift in finite systems. The discrepancy of the FSS theories
between annealed and quenched SF networks still remains in the equilibrium
Ising model, like some other nonequilibrium models. All of our analytic results
are confirmed reasonably well by numerical simulations.
