Mixed algorithms in the Ising model on directed Barabasi-Albert networks
  On directed Barabasi-Albert networks with two and seven neighbours selected by each added site, the Ising model does not seem to show a spontaneous magnetisation. Instead, the decay time for flipping of the magnetisation follows an Arrhenius law for Metropolis and Glauber algorithms, but for Wolff cluster flipping the magnetisation decays exponentially with time. On these networks the magnetisation behaviour of the Ising model, with Glauber, HeatBath,   Metropolis, Wolf or Swendsen-Wang algorithm competing against Kawasaki dynamics, is studied by Monte Carlo simulations. We show that the model exhibits the phenomenon of self-organisation (= stationary equilibrium) when   Kawasaki dynamics is not dominant in its competition with Glauber, HeatBath and Swendsen-Wang algorithms. Only for Wolff cluster flipping the magnetisation, this phenomenon occurs after an exponentially decay of magnetisation with time. The Metropolis results are independent of competition. We also study the same process of competition described above but with Kawasaki dynamics at the same temperature as the other algorithms. The obtained results are similar for Wolff cluster flipping, Metropolis and Swendsen-Wang algorithms but different for HeatBath. 
F.W.S. Lima