Microscopic model for the logarithmic size effect on the Curie point in   Barab\'asi-Albert networks
  We found that numbers of fully connected clusters in Barab\'asi-Albert (BA) networks follow the exponential distribution with the characteristic exponent $\kappa=2/m$. The critical temperature for the Ising model on the BA network is determined by the critical temperature of the largest fully connected cluster within the network. The result explains the logarithmic dependence of the critical temperature on the size of the network $N$. 
Agata Aleksiejuk-Fronczak