Opinion evolution on a BA scaling network

In this paper, the dynamics of opinion formation is investigated based on a BA (Barabási-Albert) scale-free network, using a majority-minority rule governed by parameter q. As the value of q is smoothly varied, a phase transition occurs between an ordered phase and a disordered one. By performing extensive Monte Carlo simulations, we show that the phase transition is dependent on the system size, as well as on m, the number of edges added at each time step during the growth of the BA scaling network. Additionally, some theoretical analysis is given based on mean-field theory, by neglecting fluctuations and correlations. It is observed that the theoretical results coincide with results from simulations, especially for very large m.